# Showing papers in "Journal of High Energy Physics in 2011"

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TL;DR: The ideas and the most important developments of the code are described and the capabilities of the MadGraph matrix element generator are illustrated through a few simple phenomenological examples.

Abstract: MadGraph 5 is the new version of the MadGraph matrix element generator, written in the Python programming language. It implements a number of new, efficient algorithms that provide improved performance and functionality in all aspects of the program. It features a new user interface, several new output formats including C++ process libraries for Pythia 8, and full compatibility with FeynRules for new physics models implementation, allowing for event generation for any model that can be written in the form of a Lagrangian. MadGraph 5 builds on the same philosophy as the previous versions, and its design allows it to be used as a collaborative platform where theoretical, phenomenological and simulation projects can be developed and then distributed to the high-energy community. We describe the ideas and the most important developments of the code and illustrate its capabilities through a few simple phenomenological examples.

2,684 citations

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TL;DR: In this article, the authors present a heuristic argument that shows that Newton's law of gravitation naturally arises in a theory in which space emerges through a holographic scenario and gravity is identified with an entropic force caused by changes in the information associated with the positions of material bodies.

Abstract: Starting from first principles and general assumptions we present a heuristic argument that shows that Newton’s law of gravitation naturally arises in a theory in which space emerges through a holographic scenario. Gravity is identified with an entropic force caused by changes in the information associated with the positions of material bodies. A relativistic generalization of the presented arguments directly leads to the Einstein equations. When space is emergent even Newton’s law of inertia needs to be explained. The equivalence principle auggests that it is actually the law of inertia whose origin is entropic.

1,442 citations

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TL;DR: In this article, the authors provide a derivation of holographic entanglement entropy for spherical entangling surfaces, which relies on conformally mapping the boundary CFT to a hyperbolic geometry and observing that the vacuum state is mapped to a thermal state in the latter geometry.

Abstract: We provide a derivation of holographic entanglement entropy for spherical entangling surfaces. Our construction relies on conformally mapping the boundary CFT to a hyperbolic geometry and observing that the vacuum state is mapped to a thermal state in the latter geometry. Hence the conformal transformation maps the entanglement entropy to the thermodynamic entropy of this thermal state. The AdS/CFT dictionary allows us to calculate this thermodynamic entropy as the horizon entropy of a certain topological black hole. In even dimensions, we also demonstrate that the universal contribution to the entanglement entropy is given by A-type trace anomaly for any CFT, without reference to holography.

1,399 citations

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TL;DR: In this article, a uniform treatment of rigid supersymmetric field theories in a curved spacetime was presented, focusing on four-dimensional theories with four supercharges, using classical background values of the auxiliary fields in the supergravity multiplet.

Abstract: We present a uniform treatment of rigid supersymmetric field theories in a curved spacetime \( \mathcal{M} \), focusing on four-dimensional theories with four supercharges. Our discussion is significantly simpler than earlier treatments, because we use classical background values of the auxiliary fields in the supergravity multiplet. We demonstrate our procedure using several examples. For \( \mathcal{M} = Ad{S_4} \) we reproduce the known results in the literature. A supersymmetric Lagrangian for \( \mathcal{M} = {\mathbb{S}^4} \) exists, but unless the field theory is conformal, it is not reflection positive. We derive the Lagrangian for \( \mathcal{M} = {\mathbb{S}^3} \times \mathbb{R} \) and note that the time direction \( \mathbb{R} \) can be rotated to Euclidean signature and be compactified to \( {\mathbb{S}^1} \) only when the theory has a continuous R-symmetry. The partition function on \( \mathcal{M} = {\mathbb{S}^3} \times {\mathbb{S}^1} \) is independent of the parameters of the flat space theory and depends holomorphically on some complex background gauge fields. We also consider R-invariant \( \mathcal{N} = 2 \) theories on \( {\mathbb{S}^3} \) and clarify a few points about them.

795 citations

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[...]

Fermilab

^{1}TL;DR: In this article, the authors present phenomenological results for vector boson pair production at the LHC, obtained using the parton-level next-to-leading order program MCFM, including the implementation of a new process in the code, pp → γγ, and important updates to existing processes.

Abstract: We present phenomenological results for vector boson pair production at the LHC, obtained using the parton-level next-to-leading order program MCFM. We include the implementation of a new process in the code, pp → γγ, and important updates to existing processes. We incorporate fragmentation contributions in order to allow for the experimental isolation of photons in γγ, Wγ, and Zγ production and also account for gluon-gluon initial state contributions for all relevant processes. We present results for a variety of phenomenological scenarios, at the current operating energy of √ s = 7 TeV and for the ultimate machine goal, √ s = 14 TeV. We investigate the impact of our predictions on several important distributions that enter into searches for new physics at the LHC.

790 citations

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TL;DR: In this article, the effect of trace anomalies for the Nambu-Goldstone boson of broken conformal symmetry in renormalization group flows in four dimensions is analyzed.

Abstract: We discuss some general aspects of renormalization group flows in four dimensions. Every such flow can be reinterpreted in terms of a spontaneously broken conformal symmetry. We analyze in detail the consequences of trace anomalies for the effective action of the Nambu-Goldstone boson of broken conformal symmetry. While the c-anomaly is algebraically trivial, the a-anomaly is “non-Abelian”, and leads to a positive-definite universal contribution to the S-matrix element of 2 → 2 dilaton scattering. Unitarity of the S-matrix results in a monotonically decreasing function that interpolates between the Euler anomalies in the ultraviolet and the infrared, thereby establishing the a-theorem.

777 citations

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TL;DR: In this article, a new jet shape called N-subjettiness was introduced to identify boosted hadronically-decaying objects like electroweak bosons and top quarks.

Abstract: We introduce a new jet shape—N-subjettiness—designed to identify boosted hadronically-decaying objects like electroweak bosons and top quarks. Combined with a jet invariant mass cut, N-subjettiness is an effective discriminating variable for tagging boosted objects and rejecting the background of QCD jets with large invariant mass. In efficiency studies of boostedW bosons and top quarks, we find tagging efficiencies of 30% are achievable with fake rates of 1%. We also consider the discovery potential for new heavy resonances that decay to pairs of boosted objects, and find significant improvements are possible using N-subjettiness. In this way, N-subjettiness combines the advantages of jet shapes with the discriminating power seen in previous jet substructure algorithms.

711 citations

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[...]

TL;DR: In this paper, the authors re-examine holographic versions of the c-theorem and entanglement entropy in the context of higher curvature gravity and the AdS/CFT correspondence.

Abstract: We re-examine holographic versions of the c-theorem and entanglement entropy in the context of higher curvature gravity and the AdS/CFT correspondence. We select the gravity theories by tuning the gravitational couplings to eliminate non-unitary operators in the boundary theory and demonstrate that all of these theories obey a holographic c-theorem. In cases where the dual CFT is even-dimensional, we show that the quantity that flow is the central charge associated with the A-type trace anomaly. Here, unlike in conventional holographic constructions with Einstein gravity, we are able to distinguish this quantity from other central charges or the leading coefficient in the entropy density of a thermal bath. In general, we are also able to identify this quantity with the coefficient of a universal contribution to the entanglement entropy in a particular construction. Our results suggest that these coefficients appearing in entanglement entropy play the role of central charges in odd-dimensional CFT's. We conjecture a new c-theorem on the space of odd-dimensional field theories, which extends Cardy's proposal for even dimensions. Beyond holography, we were able to show that for any even-dimensional CFT, the universal coefficient appearing the entanglement entropy which we calculate is precisely the A-type central charge.

690 citations

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TL;DR: In this paper, a factorization formula for BPS indices using attractor flow trees associated to multicentered black hole bound states was developed, which enables us to study background dependence of the BPS spectrum, to compute explicitly exact indices of various nontrivial D-brane systems, and to clarify the subtle relation of Donaldson-Thomas invariants to BPs indices of stable D6-D2-D0 states, realized in supergravity as hole halos.

Abstract: We investigate degeneracies of BPS states of D-branes on compact Calabi-Yau manifolds. We develop a factorization formula for BPS indices using attractor flow trees associated to multicentered black hole bound states. This enables us to study background dependence of the BPS spectrum, to compute explicitly exact indices of various nontrivial D-brane systems, and to clarify the subtle relation of Donaldson-Thomas invariants to BPS indices of stable D6-D2-D0 states, realized in supergravity as “hole halos.” We introduce a convergent generating function for D4 indices in the large CY volume limit, and prove it can be written as a modular average of its polar part, generalizing the fareytail expansion of the elliptic genus. We show polar states are “split” D6-anti-D6 bound states, and that the partition function factorizes accordingly, leading to a refined version of the OSV conjecture. This differs from the original conjecture in several aspects. In particular we obtain a nontrivial measure factor $ g_{\text{top}}^{{ - 2}}{e^{{ - K}}} $
and find factorization requires a cutoff. We show that the main factor determining the cutoff and therefore the error is the existence of “swing states” — D6 states which exist at large radius but do not form stable D6-anti-D6 bound states. We point out a likely breakdown of the OSV conjecture at small g
top (in the large background CY volume limit), due to the surprising phenomenon that for sufficiently large background Kahler moduli, a charge Λ Γ supporting single centered black holes of entropy ~ Λ2
S(Γ) also admits two-centered BPS black hole realizations whose entropy grows like Λ3 when Λ → ∞.

648 citations

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TL;DR: The embedding formalism for conformal field theories is developed, aimed at doing computations with symmetric traceless operators of arbitrary spin, using an indexfree notation where tensors are encoded by polynomials in auxiliary polarization vectors.

Abstract: We develop the embedding formalism for conformal field theories, aimed at doing computations with symmetric traceless operators of arbitrary spin. We use an index-free notation where tensors are encoded by polynomials in auxiliary polarization vectors. The efficiency of the formalism is demonstrated by computing the tensor structures allowed in n-point conformal correlation functions of tensors operators. Constraints due to tensor conservation also take a simple form in this formalism. Finally, we obtain a perfect match between the number of independent tensor structures of conformal correlators in d dimensions and the number of independent structures in scattering amplitudes of spinning particles in (d+1)-dimensional Minkowski space.

624 citations

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TL;DR: In this article, a simple formula relating the bulk scattering amplitudes to the asymptotic behavior of Mellin amplitudes was proposed, and it was shown that the four point Mellin amplitude is the ideal object to attempt the conformal bootstrap program in higher dimensions.

Abstract: We explore the Mellin representation of conformal correlation functions recently proposed by Mack. Examples in the AdS/CFT context reinforce the analogy between Mellin amplitudes and scattering amplitudes. We conjecture a simple formula relating the bulk scattering amplitudes to the asymptotic behavior of Mellin amplitudes and show that previous results on the flat space limit of AdS follow from our new formula. We find that the Mellin amplitudes are particularly useful in the case of conformal gauge theories in the planar limit. In this case, the four point Mellin amplitudes are meromorphic functions whose poles and their residues are entirely determined by two and three point functions of single-trace operators. This makes the Mellin amplitudes the ideal objects to attempt the conformal bootstrap program in higher dimensions.

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TL;DR: In this paper, the Lagrangian and supersymmetry rules for general supersymmetric gauge theories on squashed three-spheres preserving isometries were presented, and the partition functions are computed using localization principle, and are expressed as integrals over Coulomb branch.

Abstract: We study Euclidean 3D \( \mathcal{N} = 2 \) supersymmetric gauge theories on squashed three-spheres preserving isometries SU(2) × U(1) or U(1) × U(1) We show that, when a suitable background U(1) gauge field is turned on, these squashed spheres support charged Killing spinors and therefore \( \mathcal{N} = 2 \) supersymmetric gauge theories We present the Lagrangian and supersymmetry rules for general gauge theories The partition functions are computed using localization principle, and are expressed as integrals over Coulomb branch For the squashed sphere with U(1) × U(1) isometry, its measure and integrand are identified with the building blocks of structure constants in Liouville or Toda conformal field theories with b ≠ 1

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TL;DR: In this article, the authors extend the formula for partition functions of the superconformalgauge theory on S 3 obtained recently by Kapustin, Willett and Yaakov, to incorporate matter fields with arbitrary R-charge assignments.

Abstract: We extend theformulaforpartitionfunctions of $$\mathcal{N}=2 $$
superconformalgauge theories on S
3 obtained recently by Kapustin, Willett and Yaakov, to incorporate matter fields with arbitrary R-charge assignments. We use the result to check that the self-mirror property of $$\mathcal{N}=4 $$
SQED with two electron hypermultiplets is preserved under a certain mass deformation which breaks the supersymmetry to $$\mathcal{N}=2 $$
.

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TL;DR: In this paper, the energy-momentum tensor and charge current for charged rotating black-brane configurations up to second order in the boundary derivative expansion were derived and shown to be covariant under boundary Weyl-transformations.

Abstract: We extend the recent work on fluid-gravity correspondence to charged black-branes by determining the metric duals to arbitrary charged fluid configuration up to second order in the boundary derivative expansion. We also derive the energy-momentum tensor and the charge current for these configurations up to second order in the boundary derivative expansion. We find a new term in the charge current when there is a bulk Chern-Simons interaction thus resolving an earlier discrepancy between thermodynamics of charged rotating black holes and boundary hydrodynamics. We have also confirmed that all our expressions are covariant under boundary Weyl-transformations as expected.

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TL;DR: In this paper, the self-consistency of inflation in the Standard Model was analyzed and the authors determined the domain of energies in which this model represents a valid effective field theory as a function of the background Higgs field.

Abstract: We analyse the self-consistency of inflation in the Standard Model, where the Higgs field has a large non-minimal coupling to gravity. We determine the domain of energies in which this model represents a valid effective field theory as a function of the background Higgs field. This domain is bounded above by the cutoff scale which is found to be higher than the relevant dynamical scales throughout the whole history of the Universe, including the inflationary epoch and reheating. We present a systematic scheme to take into account quantum loop corrections to the inflationary calculations within the framework of effective field theory. We discuss the additional assumptions that must be satisfied by the ultra-violet completion of the theory to allow connection between the parameters of the inflationary effective theory and those describing the low-energy physics relevant for the collider experiments. A class of generalisations of inflationary theories with similar properties is constructed.

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TL;DR: In this paper, the free energy of the Euclidean path integrals on the three-sphere of 3-dimensional field theories is calculated using the method of localization; they reduce to certain matrix integrals that depend on the R-charges of the matter fields.

Abstract: For 3-dimensional field theories with $ \mathcal{N} = 2 $
supersymmetry the Euclidean path integrals on the three-sphere can be calculated using the method of localization; they reduce to certain matrix integrals that depend on the R-charges of the matter fields. We solve a number ofsuch large N matrix models and calculate the free energy F as a function of the trial R-charges consistent with the marginality of the super potential. In all our $ \mathcal{N} = 2 $
superconformal examples, the local maximization of F yields answers that scale as N
3/2 and agree with the dual M-theory backgrounds AdS
4 × Y, where Y are 7-dimensional Sasaki-Einstein spaces. We also find in toric examples that local F-maximization is equivalent to the minimization of the volume of Y over the space of Sasakian metrics, a procedure also referred to as Z-minimization. Moreover, we find that the functions F and Z are related for any trial R-charges. In the models we study F is positive and decreases along RG flows. We therefore propose the “F-theorem” that we hope applies to all 3-d field theories: the finite part of the free energy on the three-sphere decreases along RG trajectories and is stationary at RG fixed points. We also show that in an infinite class of Chern-Simons-matter gauge theories where the Chern-Simons levels do not sum to zero, the free energy grows as N
5/3 at large N. This non-trivial scaling matches that of the free energy of the gravity duals in type IIA string theory with Romans mass.

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TL;DR: In this paper, the de Sitter isometries imply that these correlation functions should be conformal invariant, and they also describe the general form of stress tensor correlation functions in momentum space, in a three dimensional conformal field theory.

Abstract: We consider the most general three point function for gravitational waves produced during a period of exactly de Sitter expansion. The de Sitter isometries constrain the possible shapes to only three: two preserving parity and one violating parity. These isometries imply that these correlation functions should be conformal invariant. One of the shapes is produced by the ordinary gravity action. The other shape is produced by a higher derivative correction and could be as large as the gravity contribution. The parity violating shape does not contribute to the bispectrum (1, 2), even though it is present in the wavefunction. We also introduce a spinor helicity formalism to describe de Sitter gravitational waves with circular polarization. These results also apply to correlation functions in Anti-de Sitter space. They also describe the general form of stress tensor correlation functions, in momentum space, in a three dimensional conformal field theory. Here all three shapes can arise, including the parity violating one.

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TL;DR: In this article, the authors give an explicit recursive formula for the all l-loop integrand for scattering amplitudes in the planar limit, manifesting the full Yangian symmetry of the theory.

Abstract: We give an explicit recursive formula for the all l-loop integrand for scattering amplitudes in $ \mathcal{N} = 4 $
SYM in the planar limit, manifesting the full Yangian symmetry of the theory. This generalizes the BCFW recursion relation for tree amplitudes to all loop orders, and extends the Grassmannian duality for leading singularities to the full amplitude. It also provides a new physical picture for the meaning of loops, associated with canonical operations for removing particles in a Yangian-invariant way. Loop amplitudes arise from the “entangled” removal of pairs of particles, and are naturally presented as an integral over lines in momentum-twistor space. As expected from manifest Yangian invariance, the integrand is given as a sum over non-local terms, rather than the familiar decomposition in terms of local scalar integrals with rational coefficients. Knowing the integrands explicitly, it is straightforward to express them in local forms if desired; this turns out to be done most naturally using a novel basis of chiral, tensor integrals written in momentum-twistor space, each of which has unit leading singularities. As simple illustrative examples, we present a number of new multi-loop results written in local form, including the 6- and 7-point 2-loop NMHV amplitudes. Very concise expressions are presented for all 2-loop MHV amplitudes, as well as the 5-point 3-loop MHV amplitude. The structure of the loop integrand strongly suggests that the integrals yielding the physical amplitudes are “simple”, and determined by IR-anomalies. We briefly comment on extending these ideas to more general planar theories.

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TL;DR: In this paper, the authors developed parallels between the holographic renormalization group in the bulk and the Wilsonian renormalisation group in dual field theory, and sharpened the analogy between the two sides.

Abstract: We develop parallels between the holographic renormalization group in the bulk and the Wilsonian renormalization group in the dual field theory. Our philosophy differs from most previous work on the holographic RG; the most notable feature is the key role of multi-trace operators. We work out the forms of various single-and double-trace flows. The key question, ‘what cutoff on the field theory corresponds to a radial cutoff in the bulk?’ is left unanswered, but by sharpening the analogy between the two sides we identify possible directions.

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TL;DR: In this paper, the general mass term is constructed in terms of a deformed determinant from which this property can clearly be seen, and the non-linear terms that appear in previous constructions and which do not contribute to the equations of motion are identified.

Abstract: In this work we present a systematic construction of the potentially ghost-free non-linear massive gravity actions. The most general action can be regarded as a 2-parameter deformation of a minimal massive action. Further extensions vanish in 4 dimensions. The general mass term is constructed in terms of a “deformed” determinant from which this property can clearly be seen. In addition, our formulation identifies nondynamical terms that appear in previous constructions and which do not contribute to the equations of motion. We elaborate on the formal structure of these theories as well as some of their implications.

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TL;DR: In this article, the surface charges associated with the symmetries of asymptotically flat four dimensional spacetimes at null infinity are constructed, and they realize the symmetry algebra in general only up to a field-dependent central extension that satisfies a suitably generalized cocycle condition.

Abstract: The surface charges associated with the symmetries of asymptotically flat four dimensional spacetimes at null infinity are constructed. They realize the symmetry algebra in general only up to a field-dependent central extension that satisfies a suitably generalized cocycle condition. This extension vanishes when using the globally well defined BMS algebra. For the Kerr black hole and the enlarged BMS algebra with both supertranslations and superrotations, some of the supertranslation charges diverge whereas there are no divergences for the superrotation charges. The central extension is proportional to the rotation parameter and involves divergent integrals on the sphere.

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TL;DR: In this paper, it was shown that the near-extremal solutions of EMD theories, studied in ArXiv:1005.4690, provide IR quantum critical geometries, by embedding classes of them in higher-dimensional AdS and Lifshitz solutions.

Abstract: We show that the near-extremal solutions of Einstein-Maxwell-Dilaton theories, studied in ArXiv:1005.4690, provide IR quantum critical geometries, by embedding classes of them in higher-dimensional AdS and Lifshitz solutions. This explains the scaling of their thermodynamic functions and their IR transport coefficients, the nature of their spectra, the Gubser bound, and regulates their singularities. We propose that these are the most general quantum critical IR asymptotics at finite density of EMD theories.

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TL;DR: In this article, the authors examine several consistency issues present in three non-relativistic gravity theories: Hořava's projectable theory, the healthy non-projectable extension, and a new extension related to ghost condensation.

Abstract: Hořava’s proposal for non-relativistic quantum gravity introduces a preferred time foliation of space-time which violates the local Lorentz invariance. The foliation is encoded in a dynamical scalar field which we call ‘khronon’. The dynamics of the khronon field is sensitive to the symmetries and other details of the particular implementations of the proposal. In this paper we examine several consistency issues present in three non-relativistic gravity theories: Hořava’s projectable theory, the healthy non-projectable extension, and a new extension related to ghost condensation. We find that the only model which is free from instabilities and strong coupling is the non-projectable one. We elaborate on the phenomenology of the latter model including a discussion of the couplings of the khronon to matter. In particular, we obtain the parameters of the post-Newtonian expansion in this model and show that they are compatible with current observations.

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TL;DR: In this paper, the authors reformulate ten-dimensional type II supergravity as a generalised geometrical analogue of Einstein gravity, defined by an O(9, 1) × O(1, 9) ⊂ O(10, 10) × $ {\mathbb{R}^{+} } $ structure on the generalised tangent space.

Abstract: We reformulate ten-dimensional type II supergravity as a generalised geometrical analogue of Einstein gravity, defined by an O(9, 1) × O(1, 9) ⊂ O(10, 10) × $ {\mathbb{R}^{+} } $
structure on the generalised tangent space. Using the notion of generalised connection and torsion, we introduce the analogue of the Levi-Civita connection, and derive the corresponding tensorial measures of generalised curvature. We show how, to leading order in the fermion fields, these structures allow one to rewrite the action, equations of motion and supersymmetry variations in a simple, manifestly Spin(9, 1) × Spin(1, 9)-covariant form. The same formalism also describes d-dimensional compactifications to flat space.

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TL;DR: In this article, it was shown that in general Liouville's equations do not have enough complex-valued solutions to account for the semiclassical behavior of the DOZZ formula.

Abstract: Correlation functions in Liouville theory are meromorphic functions of the Liouville momenta, as is shown explicitly by the DOZZ formula for the three-point function on S2. In a certain physical region, where a real classical solution exists, the semiclassical limit of the DOZZ formula is known to agree with what one would expect from the action of the classical solution. In this paper, we ask what happens outside of this physical region. Perhaps surprisingly we find that, while in some range of the Liouville momenta the semiclassical limit is associated to complex saddle points, in general Liouville’s equations do not have enough complex-valued solutions to account for the semiclassical behavior. For a full picture, we either must include “solutions” of Liouville’s equations in which the Liouville field is multivalued (as well as being complex-valued), or else we can reformulate Liouville theory as a Chern-Simons theory in three dimensions, in which the requisite solutions exist in a more conventional sense. We also study the case of “timelike” Liouville theory, where we show that a proposal of Al. B. Zamolodchikov for the exact three-point function on S2 can be computed by the original Liouville path integral evaluated on a new integration cycle.

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TL;DR: In this paper, the authors examined holographic entanglement entropy with higher curvature gravity in the bulk and showed that in general Wald's formula for horizon entropy does not yield the correct entropy.

Abstract: We examine holographic entanglement entropy with higher curvature gravity in the bulk. We show that in general Wald’s formula for horizon entropy does not yield the correct entanglement entropy. However, for Lovelock gravity, there is an alternate prescription which involves only the intrinsic curvature of the bulk surface. We verify that this prescription correctly reproduces the universal contribution to the entanglement entropy for CFT’s in four and six dimensions. We also make further comments on gravitational theories with more general higher curvature interactions.

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TL;DR: The gradient flow in non-abelian gauge theories is defined by a local diffusion equation that evolves the gauge field as a function of the flow time in a gauge-covariant manner as mentioned in this paper.

Abstract: The gradient flow in non-abelian gauge theories on \( {\mathbb{R}^4} \) is defined by a local diffusion equation that evolves the gauge field as a function of the flow time in a gauge-covariant manner. Similarly to the case of the Langevin equation, the correlation functions of the time-dependent field can be expanded in perturbation theory, the Feynman rules being those of a renormalizable field theory on \( {\mathbb{R}^4} \times \left[ {0,\infty } \right) \). For any matter multiplet and to all loop orders, we show that the correlation functions are finite, i.e. do not require additional renormalization, once the theory in four dimensions is renormalized in the usual way. The flow thus maps the gauge field to a one-parameter family of smooth renormalized fields.

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TL;DR: For conformal field theories in arbitrary dimensions, this paper introduced a method to derive the conformal blocks corresponding to the exchange of a traceless symmetric tensor appearing in four point functions of operators with spin.

Abstract: For conformal field theories in arbitrary dimensions, we introduce a method to derive the conformal blocks corresponding to the exchange of a traceless symmetric tensor appearing in four point functions of operators with spin. Using the embedding space formalism, we show that one can express all such conformal blocks in terms of simple differential operators acting on the basic scalar conformal blocks. This method gives all conformal blocks for conformal field theories in three dimensions. We demonstrate how this formalism can be applied in a few simple examples.

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TL;DR: In this article, it was shown that the Mellin space is the natural home for correlation functions in CFTs with weakly coupled bulk duals, and that these correlators have poles corresponding to an OPE decomposition into left and right sub-correlators.

Abstract: We provide dramatic evidence that ‘Mellin space’ is the natural home for correlation functions in CFTs with weakly coupled bulk duals. In Mellin space, CFT correlators have poles corresponding to an OPE decomposition into ‘left’ and ‘right’ sub-correlators, in direct analogy with the factorization channels of scattering amplitudes. In the regime where these correlators can be computed by tree level Witten diagrams in AdS, we derive an explicit formula for the residues of Mellin amplitudes at the corresponding factorization poles, and we use the conformal Casimir to show that these amplitudes obey algebraic finite difference equations. By analyzing the recursive structure of our factorization formula we obtain simple diagrammatic rules for the construction of Mellin amplitudes corresponding to tree-level Witten diagrams in any bulk scalar theory. We prove the diagrammatic rules using our finite difference equations. Finally, we show that our factorization formula and our diagrammatic rules morph into the flat space S-Matrix of the bulk theory, reproducing the usual Feynman rules, when we take the flat space limit of AdS/CFT. Throughout we emphasize a deep analogy with the properties of flat space scattering amplitudes in momentum space, which suggests that the Mellin amplitude may provide a holographic definition of the flat space S-Matrix.

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TL;DR: In this article, the authors reformulate the Hamiltonian form of bosonic eleven-dimensional supergravity in terms of an object that unifies the three-form and the metric.

Abstract: We reformulate the Hamiltonian form of bosonic eleven dimensional supergravity in terms of an object that unifies the three-form and the metric. For the case of four spatial dimensions, the duality group is manifest and the metric and C-field are on an equal footing even though no dimensional reduction is required for our results to hold. One may also describe our results using the generalized geometry that emerges from membrane duality. The relationship between the twisted Courant algebra and the gauge symmetries of eleven dimensional supergravity are described in detail.