Showing papers on "AdS/CFT correspondence published in 2010"

Exact results for Wilson loops in superconformal Chern-Simons theories with matter

Abstract: We use localization techniques to compute the expectation values of supersymmetric Wilson loops in Chern-Simons theories with matter. We find the path-integral reduces to a non-Gaussian matrix model. The Wilson loops we consider preserve a single complex supersymmetry, and exist in any N = 2 theory, though the localization requires superconformal symmetry. We present explicit results for the cases of pure Chern-Simons theory with gauge group U(N), showing agreement with the known results, and ABJM, showing agreement with perturbative calculations. Our method applies to other theories, such as Gaiotto-Witten theories, BLG, and their variants.

Aspects of the BMS/CFT correspondence

Abstract: After a review of symmetries and classical solutions involved in the AdS3/CFT2 correspondence, we apply a similar analysis to asymptotically flat spacetimes at null infinity in 3 and 4 dimensions. In the spirit of two dimensional conformal field theory, the symmetry algebra of asymptotically flat spacetimes at null infinity in 4 dimensions is taken to be the semi-direct sum of supertranslations with infinitesimal local conformal transformations and not, as usually done, with the Lorentz algebra. As a first application, we derive how the symmetry algebra is realized on solution space. In particular, we work out the behavior of Bondi’s news tensor, mass and angular momentum aspects under local conformal transformations.

Effective Holographic Theories for low-temperature condensed matter systems

Abstract: The IR dynamics of effective holographic theories capturing the interplay between charge density and the leading relevant scalar operator at strong coupling are analyzed. Such theories are parameterized by two real exponents (γ, δ) that control the IR dynamics. By studying the thermodynamics, spectra and conductivities of several classes of charged dilatonic black hole solutions that include the charge density back reaction fully, the landscape of such theories in view of condensed matter applications is characterized. Several regions of the (γ, δ) plane can be excluded as the extremal solutions have unacceptable singularities. The classical solutions have generically zero entropy at zero temperature, except when γ = δ where the entropy at extremality is finite. The general scaling of DC resistivity with temperature at low temperature, and AC conductivity at low frequency and temperature across the whole (γ, δ) plane, is found. There is a codimension-one region where the DC resistivity is linear in the temperature. For massive carriers, it is shown that when the scalar operator is not the dilaton, the DC resistivity scales as the heat capacity (and entropy) for planar (3d) systems. Regions are identified where the theory at finite density is a Mott-like insulator at T = 0. We also find that at low enough temperatures the entropy due to the charge carriers is generically larger than at zero charge density.

Holographic Duality with a View Toward Many-Body Physics

Abstract: These are notes based on a series of lectures given at the KITP workshop Quantum Criticality and the AdS/CFT Correspondence in July, 2009. The goal of the lectures was to introduce condensed matter physicists to the AdS/CFT correspondence. Discussion of string theory and of supersymmetry is avoided to the extent possible.

Quantum gravity partition functions in three dimensions

Abstract: We consider pure three-dimensional quantum gravity with a negative cosmological constant. The sum of known contributions to the partition function from classical geometries can be computed exactly, including quantum corrections. However, the result is not physically sensible, and if the model does exist, there are some additional contributions. One possibility is that the theory may have long strings and a continuous spectrum. Another possibility is that complex geometries need to be included, possibly leading to a holomorphically factorized partition function. We analyze the subleading corrections to the Bekenstein-Hawking entropy and show that these can be correctly reproduced in such a holomorphically factorized theory. We also consider the Hawking-Page phase transition between a thermal gas and a black hole and show that it is a phase transition of Lee-Yang type, associated with a condensation of zeros in the complex temperature plane. Finally, we analyze pure three-dimensional supergravity, with similar results.

Towards Strange Metallic Holography

Abstract: We initiate a holographic model building approach to `strange metallic' phenomenology. Our model couples a neutral Lifshitz-invariant quantum critical theory, dual to a bulk gravitational background, to a finite density of gapped probe charge carriers, dually described by D-branes. In the physical regime of temperature much lower than the charge density and gap, we exhibit anomalous scalings of the temperature and frequency dependent conductivity. Choosing the dynamical critical exponent z appropriately we can match the non-Fermi liquid scalings, such as linear resistivity, observed in strange metal regimes. As part of our investigation we outline three distinct string theory realizations of Lifshitz geometries: from F theory, from polarised branes, and from a gravitating charged Fermi gas. We also identify general features of renormalisation group ow in Lifshitz theories, such as the appearance of relevant charge-charge interactions when z ≥ 2. We outline a program to extend this model building approach to other anomalous observables of interest such as the Hall conductivity.

Higher spin gauge theory and holography: the three-point functions

Abstract: In this paper we calculate the tree level three-point functions of Vasiliev's higher spin gauge theory in AdS4 and find agreement with the correlators of the free field theory of N massless scalars in three dimensions in the O(N) singlet sector. This provides substantial evidence that Vasiliev theory is dual to the free field theory, thus verifying a conjecture of Klebanov and Polyakov. We also find agreement with the critical O(N) vector model, when the bulk scalar field is subject to the alternative boundary condition such that its dual operator has classical dimension 2.

Exact Spectrum of Anomalous Dimensions of Planar N=4 Supersymmetric Yang-Mills Theory: TBA and excited states

Abstract: Using the thermodynamic Bethe ansatz method we derive an infinite set of integral non-linear equations for the spectrum of states/operators in AdS/CFT. The Y-system conjectured in Gromov et al. (Integrability for the Full Spectrum of Planar AdS/CFT. arXiv:0901.3753 [hep-th]) for the spectrum of all operators in planar N = 4 SYM theory follows from these equations. In particular, we present the integral TBA type equations for the spectrum of all operators within the sl(2) sector. We prove that all the kernels and free terms entering these TBA equations are real and have nice fusion properties in the relevant mirror kinematics. We find the analog of DHM formula for the dressing kernel in the mirror kinematics.

Nonlinear W ∞ as asymptotic symmetry of three-dimensional higher spin AdS gravity

Abstract: We investigate the asymptotic symmetry algebra of (2+1)-dimensional higher spin, anti-de Sitter gravity. We use the formulation of the theory as a Chern-Simons gauge theory based on the higher spin algebra hs(1, 1). Expanding the gauge connection around asymptotically anti-de Sitter spacetime, we specify consistent boundary conditions on the higher spin gauge fields. We then study residual gauge transformation, the corresponding surface terms and their Poisson bracket algebra. We find that the asymptotic symmetry algebra is a nonlinearly realized W ∞ algebra with classical central charges. We discuss implications of our results to quantum gravity and to various situations in string theory.

Holographic evolution of entanglement entropy

Abstract: We study the evolution of entanglement entropy in a 2-dimensional equilibration process that has a holographic description in terms of a Vaidya geometry. It models a unitary evolution in which the field theory starts in a pure state, its vacuum, and undergoes a perturbation that brings it far from equilibrium. The entanglement entropy in this set up provides a measurement of the quantum entanglement in the system. Using holographic techniques we recover the same result obtained before from the study of processes triggered by a sudden change in a parameter of the hamiltonian, known as quantum quenches. Namely, entanglement in 2-dimensional conformal field theories propagates with velocity v2 = 1 [1]. Both in quantum quenches and in the Vaidya model equilibration is only achieved at the local level. Remarkably, the holographic derivation of this last fact requires information from behind the apparent horizon generated in the process of gravitational collapse described by the Vaidya geometry. In the early stages of the evolution the apparent horizon seems however to play no relevant role with regard to the entanglement entropy. We speculate on the possibility of deriving a thermalization time for occupation numbers from our analysis.

Holography of Charged Dilaton Black Holes

Abstract: We study charged dilaton black branes in AdS 4. Our system involves a dilaton ϕ coupled to a Maxwell field F μν with dilaton-dependent gauge coupling, $ \frac{1}{{{g^2}}} = {f^2}\left( \phi \right) $ . First, we find the solutions for extremal and near extremal branes through a combination of analytical and numerical techniques. The near horizon geometries in the simplest cases, where f(ϕ) = e αϕ , are Lifshitz-like, with a dynamical exponent z determined by α. The black hole thermodynamics varies in an interesting way with α, but in all cases the entropy is vanishing and the specific heat is positive for the near extremal solutions. We then compute conductivity in these backgrounds. We find that somewhat surprisingly, the AC conductivity vanishes like ω 2 at T = 0 independent of α. We also explore the charged black brane physics of several other classes of gauge-coupling functions f(ϕ). In addition to possible applications in AdS/CMT, the extremal black branes are of interest from the point of view of the attractor mechanism. The near horizon geometries for these branes are universal, independent of the asymptotic values of the moduli, and describe generic classes of endpoints for attractor flows which are different from AdS 2 × R 2.

Holographic GB gravity in arbitrary dimensions

Abstract: We study the properties of the holographic CFT dual to Gauss-Bonnet gravity in general D(≥ 5) dimensions. We establish the AdS/CFT dictionary and in particular relate the couplings of the gravitational theory to the universal couplings arising in correlators of the stress tensor of the dual CFT. This allows us to examine constraints on the gravitational couplings by demanding consistency of the CFT. In particular, one can demand positive energy fluxes in scattering processes or the causal propagation of fluctuations. We also examine the holographic hydrodynamics, commenting on the shear viscosity as well as the relaxation time. The latter allows us to consider causality constraints arising from the second-order truncated theory of hydrodynamics.

Correspondence between asymptotically flat spacetimes and nonrelativistic conformal field theories.

Abstract: We find a surprising connection between asymptotically flat spacetimes and nonrelativistic conformal systems in one lower dimension. The Bondi-Metzner-Sachs (BMS) group is the group of asymptotic isometries of flat Minkowski space at null infinity. This is known to be infinite dimensional in three and four dimensions. We show that the BMS algebra in 3 dimensions is the same as the 2D Galilean conformal algebra (GCA) which is of relevance to nonrelativistic conformal symmetries. We further justify our proposal by looking at a Penrose limit on a radially infalling null ray inspired by nonrelativistic scaling and obtain a flat metric. The BMS4 algebra is also discussed and found to be the same as another class of GCA, called semi-GCA, in three dimensions. We propose a general BMS-GCA correspondence. Some consequences are discussed.

Exact results in ABJM theory from topological strings

Abstract: Recently, Kapustin, Willett and Yaakov have found, by using localization techniques, that vacuum expectation values of Wilson loops in ABJM theory can be calculated with a matrix model. We show that this matrix model is closely related to Chern-Simons theory on a lens space with a gauge supergroup. This theory has a topological string large N dual, and this makes possible to solve the matrix model exactly in the large N expansion. In particular, we find the exact expression for the vacuum expectation value of a 1/6 BPS Wilson loop in the ABJM theory, as a function of the 't Hooft parameters, and in the planar limit. This expression gives an exact interpolating function between the weak and the strong coupling regimes. The behavior at strong coupling is in precise agreement with the prediction of the AdS string dual. We also give explicit results for the 1/2 BPS Wilson loop recently constructed by Drukker and Trancanelli.

Supersymmetric AdS 4 black holes and attractors

Abstract: Using the general recipe given in arXiv:0804.0009, where all timelike supersymmetric solutions of $ \mathcal{N} = 2 $ , D = 4 gauged supergravity coupled to abelian vector multiplets were classified, we construct the first examples of genuine supersymmetric black holes in AdS4 with nonconstant scalar fields. This is done for various choices of the prepotential, amongst others for the STU model. These solutions permit to study the BPS attractor flow in AdS. We also determine the most general supersymmetric static near-horizon geometry and obtain the attractor equations in gauged supergravity. As a general feature we find the presence of flat directions in the black hole potential, i.e., generically the values of the moduli on the horizon are not completely specified by the charges. For one of the considered prepotentials, the resulting moduli space is determined explicitely. Still, in all cases, we find that the black hole entropy depends only on the charges, in agreement with the attractor mechanism.

Six-dimensional Methods for Four-dimensional Conformal Field Theories

Abstract: The calculation of both spinor and tensor Green's functions in four-dimensional conformally-invariant field theories can be greatly simplified by six-dimensional methods. For this purpose, four-dimensional fields are constructed as projections of fields on the hypercone in six-dimensional projective space, satisfying certain transversality conditions. In this way some Green's functions in conformal field theories are shown to have structures more general than those commonly found by use of the inversion operator. These methods fit in well with the assumption of AdS/CFT duality. In particular, it is transparent that if fields on ${\mathrm{AdS}}_{5}$ approach finite limits on the boundary of ${\mathrm{AdS}}_{5}$, then in the conformal field theory on this boundary these limits transform with conformal dimensionality zero if they are tensors (of any rank), but with conformal dimension $1/2$ if they are spinors or spinor-tensors.

Holography of dyonic dilaton black branes

Abstract: We study black branes carrying both electric and magnetic charges in Einstein-Maxwell theory coupled to a dilaton-axion in asymptotically anti de Sitter space. After reviewing and extending earlier results for the case of electrically charged branes, we characterise the thermodynamics of magnetically charged branes. We then focus on dyonic branes in theories which enjoy an SL(2,R) electric-magnetic duality. Using SL(2,R), we are able to generate solutions with arbitrary charges starting with the electrically charged solution, and also calculate transport coefficients. These solutions all exhibit a Lifshitz-like near-horizon geometry. The system behaves as expected for a charged fluid in a magnetic field, with non-vanishing Hall conductance and vanishing DC longitudinal conductivity at low temperatures. Its response is characterised by a cyclotron resonance at a frequency proportional to the magnetic field, for small magnetic fields. Interestingly, the DC Hall conductance is related to the attractor value of the axion. We also study the attractor flows of the dilaton-axion, both in cases with and without an additional modular-invariant scalar potential. The flows exhibit intricate behaviour related to the duality symmetry. Finally, we briefly discuss attractor flows in more general dilaton-axion theories which do not enjoy SL(2,R) symmetry.

Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity

Abstract: We explore the relation between positivity of the energy constraints in conformal field theories and causality in their dual gravity description. Our discussion involves CFTs with different central charges whose description, in the gravity side, requires the inclusion of quadratic curvature corrections. It is enough, indeed, to consider the Gauss-Bonnet term. We find that both sides of the AdS/CFT correspondence impose a restriction on the Gauss-Bonnet coupling. In the case of 6d supersymmetric CFTs, we show the full matching of these restrictions. We perform this computation in two ways. First by considering a thermal setup in a black hole background. Second by scrutinizing the scattering of gravitons with a shock wave in AdS. The different helicities provide the corresponding lower and upper bounds. We generalize these results to arbitrary higher dimensions and comment on some hints and puzzles they prompt regarding the possible existence of higher dimensional CFTs and the extent to which the AdS/CFT correspondence would be valid for them.

Black hole superradiance from Kerr/CFT

Abstract: The superradiant scattering of a scalar field with frequency and angular momentum (ω, m) by a near-extreme Kerr black hole with mass and spin (M, J) was derived in the seventies by Starobinsky, Churilov, Press and Teukolsky. In this paper we show that for frequencies scaled to the superradiant bound the full functional dependence on (ω, m, M, J) of the scattering amplitudes is precisely reproduced by a dual two-dimensional conformal field theory in which the black hole corresponds to a specific thermal state and the scalar field to a specific operator. This striking agreement corroborates a conjectured Kerr/CFT correspondence.

Sicilian gauge theories and N=1 dualities

Abstract: In theories without known Lagrangian descriptions, knowledge of the global symmetries is often one of the few pieces of information we have at our disposal. Gauging (part of) such global symmetries can then lead to interesting new theories, which are usually still quite mysterious. In this work, we describe a set of tools that can be used to explore the superconformal phases of these theories. In particular, we describe the contribution of such non-Lagrangian sectors to the NSVZ β-function, and elucidate the counting of marginal deformations. We apply our techniques to $$ \mathcal{N} $$ = 1 theories obtained by mass deformations of the $$ \mathcal{N} $$ = 2 conformal theories recently found by Gaiotto. Because the basic building block of these theories is a triskelion, or trivalent vertex, we dub them “Sicilian gauge theories.” We identify these $$ \mathcal{N} $$ = 1 theories as compactifications of the six-dimensional A N (2, 0) theory on Riemann surfaces with punctures and SU(2) Wilson lines. These theories include the holographic duals of the $$ \mathcal{N} $$ = 1 supergravity solutions found by Maldacena and Nunez.

Integrability and the AdS 3/CFT 2 correspondence

Abstract: We investigate the AdS 3/CFT 2 correspondence for theories with 16 supercharges using the integrability approach. We construct Green-Schwarz actions for Type IIB strings on AdS 3 × S 3× M 4 where M 4 = T 4 or S 3 × S 1 using the coset approach. These actions are based on a Z4 automorphism of the super-coset D(2, 1; α) × D(2, 1; α)/SO(1, 2) × SO(3)×SO(3). The equations of motion admit a representation in terms of a Lax connection, showing that the system is classically integrable. We present the finite gap equations for these actions. When α = 0, 1/2, 1 we propose a set of quantum Bethe equations valid at all values of the coupling. The AdS 3/CFT 2 duals contain novel massless modes whose role remains to be explored.

On the existence of meta-stable vacua in Klebanov-Strassler

Abstract: We solve for the complete space of linearized deformations of the Klebanov-Strassler background consistent with the symmetries preserved by a stack of anti-D3 branes smeared on the S3 of the deformed conifold. We find that the only solution whose UV physics is consistent with that of a perturbation produced by anti-D3 branes must have a singularity in the infrared, coming from NS and RR three-form field strengths whose energy density diverges. If this singularity is admissible, our solution describes the backreaction of the anti-D3 branes, and is thus likely to be dual to the conjectured metastable vacuum in the Klebanov-Strassler field theory. If this singularity is not admissible, then our analysis strongly suggests that anti-D3 branes do not give rise to metastable Klebanov-Strassler vacua, which would have dramatic consequences for some string theory constructions of de Sitter space. Key to this result is a simple, universal form for the force on a probe D3-brane in our ansatz.

Condensed Matter and AdS/CFT

Abstract: I review two classes of strong coupling problems in condensed matter physics, and describe insights gained by application of the AdS/CFT correspondence. The first class concerns non-zero temperature dynamics and transport in the vicinity of quantum critical points described by relativistic field theories. I describe how relativistic structures arise in models of physical interest, present results for their quantum critical crossover functions and magneto-thermoelectric hydrodynamics. The second class concerns symmetry breaking transitions of two-dimensional systems in the presence of gapless electronic excitations at isolated points or along lines (i.e. Fermi surfaces) in the Brillouin zone. I describe the scaling structure of a recent theory of the Ising-nematic transition in metals, and discuss its possible connection to theories of Fermi surfaces obtained from simple AdS duals.

Holographic superconductor/insulator transition at zero temperature

Abstract: We analyze the five-dimensional AdS gravity coupled to a gauge field and a charged scalar field. Under a Scherk-Schwarz compactification, we show that the system undergoes a superconductor/insulator transition at zero temperature in 2 + 1 dimensions as we change the chemical potential. By taking into account a confinement/deconfinement transition, the phase diagram turns out to have a rich structure. We will observe that it has a similarity with the RVB (resonating valence bond) approach to high-Tc superconductors via an emergent gauge symmetry.

Exact spectrum of planar N=4 supersymmetric Yang-Mills theory: Konishi dimension at any coupling.

Abstract: We compute the full dimension of the Konishi operator in planar N=4 super Yang-Mills theory for a wide range of couplings, from weak to strong coupling regime, and predict the subleading terms in its strong coupling asymptotics. For this purpose we solve numerically the integral form of the AdS/CFT Y-system equations for the exact energies of excited states proposed by us and A. Kozak.

Quantum criticality and holographic superconductors in M-theory

Abstract: We present a consistent Kaluza-Klein truncation of D = 11 supergravity on an arbitrary seven-dimensional Sasaki-Einstein space (SE7) to a D = 4 theory containing a metric, a gauge-eld, a complex scalar eld and a real scalar eld. We use this D = 4 theory to construct various black hole solutions that describe the thermodynamics of the d = 3 CFTs dual to skew-whied AdS4 SE7 solutions. We show that these CFTs have a rich phase diagram, including holographic superconductivity with, generically, broken parity and time reversal invariance. At zero temperature the superconducting solutions are charged domain walls with a universal emergent conformal symmetry in the far infrared.

Form factors at strong coupling via a Y-system

Abstract: We compute form factors in planar $ \mathcal{N} = 4 $ Super Yang-Mills at strong coupling. Namely we consider the overlap between an operator insertion and 2n gluons. Through the gauge/string duality these are given by minimal surfaces in AdS space. The surfaces end on an infinite periodic sequence of null segments at the boundary of AdS. We consider surfaces that can be embedded in AdS 3. We derive set of functional equations for the cross ratios as functions of the spectral parameter. These equations are of the form of a Y-system. The integral form of the Y-system has Thermodynamics Bethe Ansatz form. The area is given by the free energy of the TBA system or critical value of Yang-Yang functional. We consider a restricted set of operators which have small conformal dimension compared to $ \sqrt {{{\uplambda }}} $ .

Holographic three-point functions of semiclassical states

Abstract: We calculate the holographic three-point functions in $ \mathcal{N} = 4 $ super-Yang-Mills theory in the case when two of the operators are semiclassical and one is dual to a supergravity mode. We further discuss the transition to the regime when all three operators are semiclassical.

AdS7/CFT6, Gauss-Bonnet gravity, and viscosity bound

Abstract: We study the relation between the causality and positivity of energy bounds for Gauss-Bonnet gravity in an AdS 7 background. Requiring the group velocity of metastable states to be bounded by the speed of light places a bound on the value of Gauss-Bonnet coupling. To find the positivity of energy constraints we compute the parameters which determine the angular distribution of the energy flux in terms of three independent coefficients specifying the three-point function of the stress-energy tensor. We then relate the latter to the Weyl anomaly of the six-dimensional CFT and compute the anomaly holographically. The resulting upper bound on the Gauss-Bonnet coupling coincides with that from causality and results in a new bound on viscosity/entropy ratio.