Recently, it has been proposed by Maldacena that large $N$ limits of certain conformal field theories in $d$ dimensions can be described in terms of supergravity (and string theory) on the product of $d+1$-dimensional $AdS$ space with a compact manifold. Here we elaborate on this idea and propose a precise correspondence between conformal field theory observables and those of supergravity: correlation functions in conformal field theory are given by the dependence of the supergravity action on the asymptotic behavior at infinity. In particular, dimensions of operators in conformal field theory are given by masses of particles in supergravity. As quantitative confirmation of this correspondence, we note that the Kaluza-Klein modes of Type IIB supergravity on $AdS_5\times {\bf S}^5$ match with the chiral operators of ${\cal N}=4$ super Yang-Mills theory in four dimensions. With some further assumptions, one can deduce a Hamiltonian version of the correspondence and show that the ${\cal N}=4$ theory has a large $N$ phase transition related to the thermodynamics of $AdS$ black holes.

/pdf/anti-de-sitter-space-and-holography-58a7vi1qn6.pdf

Anti De Sitter Space And Holography

Recently, it has been proposed by Maldacena that large $N$ limits of certain conformal field theories in $d$ dimensions can be described in terms of supergravity (and string theory) on the product of $d+1$-dimensional $AdS$ space with a compact manifold. Here we elaborate on this idea and propose a precise correspondence between conformal field theory observables and those of supergravity: correlation functions in conformal field theory are given by the dependence of the supergravity action on the asymptotic behavior at infinity. In particular, dimensions of operators in conformal field theory are given by masses of particles in supergravity. As quantitative confirmation of this correspondence, we note that the Kaluza-Klein modes of Type IIB supergravity on $AdS_5\times {\bf S}^5$ match with the chiral operators of $\N=4$ super Yang-Mills theory in four dimensions. With some further assumptions, one can deduce a Hamiltonian version of the correspondence and show that the $\N=4$ theory has a large $N$ phase transition related to the thermodynamics of $AdS$ black holes.

Anti de sitter space and holography

We discuss the theoretical bases that underpin the automation of the computations of tree-level and next-to-leading order cross sections, of their matching to parton shower simulations, and of the merging of matched samples that differ by light-parton multiplicities. We present a computer program, MadGraph5 aMC@NLO, capable of handling all these computations — parton-level fixed order, shower-matched, merged — in a unified framework whose defining features are flexibility, high level of parallelisation, and human intervention limited to input physics quantities. We demonstrate the potential of the program by presenting selected phenomenological applications relevant to the LHC and to a 1-TeV e + e − collider. While next-to-leading order results are restricted to QCD corrections to SM processes in the first public version, we show that from the user viewpoint no changes have to be expected in the case of corrections due to any given renormalisable Lagrangian, and that the implementation of these are well under way.

/pdf/the-automated-computation-of-tree-level-and-next-to-leading-4etm0g6w46.pdf

The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations

http://inspirehep.net/record/499969/files/arXiv:hep-th_9905111.pdf

Large N Field Theories, String Theory and Gravity

This is an updated version of supplementary information to accompany "Quantum supremacy using a programmable superconducting processor", an article published in the October 24, 2019 issue of Nature. The main article is freely available at this https URL. Summary of changes since arXiv:1910.11333v1 (submitted 23 Oct 2019): added URL for qFlex source code; added Erratum section; added Figure S41 comparing statistical and total uncertainty for log and linear XEB; new References [1,65]; miscellaneous updates for clarity and style consistency; miscellaneous typographical and formatting corrections.

/pdf/supplementary-information-for-quantum-supremacy-using-a-3tkhfafpzk.pdf

Supplementary information for "Quantum supremacy using a programmable superconducting processor"

It is shown that a wide class of non-Abelian gauge theories have, up to calculable logarithmic corrections, free-field-theory asymptotic behavior. It is suggested that Bjorken scaling may be obtained from strong-interaction dynamics based on non-Abelian gauge symmetry.

https://link.aps.org/pdf/10.1103/PhysRevLett.30.1343

Ultraviolet Behavior of Non-Abelian Gauge Theories

The current understanding of the behavior of quantum chromodynamics at finite temperature is presented. Perturbative methods are used to explore the high-temperature dynamics. At sufficiently high temperatures the plasma of thermal excitations screens all color electric fields and quarks are unconfined. It is believed that the high-temperature theory develops a dynamical mass gap. However in perturbation theory the infrared behavior of magnetic fluctuations is so singular that beyond some order the perturbative expansion breaks down. The topological classification of finite-energy, periodic fields is presented and the classical solutions which minimize the action in each topological sector are examined. These include periodic instantons and magnetic monopoles. At sufficiently high temperature only fields with integral topological charge can contribute to the functional integral. Electric screening completely suppresses the contribution of fields with nonintegral topological charge. Consequently the $\ensuremath{\theta}$ dependence of the free energy at high temperature is dominated by the contribution of instantons. The complete temperature dependence of the instanton density is explicitly computed and large-scale instantons are found to be suppressed. Therefore the effects of instantons may be reliably calculated at sufficiently high temperature. The behavior of the theory in the vicinity of the transition from the high-temperature quark phase to the low-temperature hadronic phase cannot be accurately computed. However, at least in the absence of light quarks, semiclassical techniques and lattice methods may be combined to yield a simple picture of the dynamics valid for both high and low temperature, and to estimate the transition temperature.

QCD and instantons at finite temperature

Two-dimensional massless fermion field theories with quartic interactions are analyzed. These models are asymptotically free. The models are expanded in powers of $\frac{1}{N,}$ where $N$ is the number of components of the fermion field. In such an expansion one can explicitly sum to all orders in the coupling constants. It is found that dynamical symmetry breaking occurs in these models for any value of the coupling constant. The resulting theories produce a fermion mass dynamically, in addition to a scalar bound state and, if the broken symmetry is continuous, a Goldstone boson. The resulting theories contain no adjustable parameters. The search for symmetry breaking is performed using functional techniques, the new feature here being that a composite field, say $\overline{\ensuremath{\psi}}\ensuremath{\psi}$, develops a nonvanishing vacuum expectation value. The "potential" of composite fields is discussed and constructed. General results are derived for arbitrary theories in which all masses are generated dynamically. It is proved that in asymptotically free theories the dynamical masses must depend on the coupling constants in a nonanalytic fashion, vanishing exponentially when these vanish. It is argued that infrared-stable theories, such as massless-fermion quantum electrodynamics, cannot produce masses dynamically. Four-dimensional scalar field theories with quartic interactions are analyzed in the large-$N$ limit and are shown to yield unphysical results. The models are extended to include gauge fields. It is then found that the gauge vector mesons acquire a mass through a dynamical Higgs mechanism. The higher-order corrections, of order $\frac{1}{N}$, to the models are analyzed. Essential singularities, of the Borel-summable type, are discovered at zero coupling constant. The origin of the singularities is the ultraviolet behavior of the theory.

Dynamical symmetry breaking in asymptotically free field theories

Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization-group techniques and their application to scaling phenomena. The renormalization-group equations are derived for Yang-Mills theories. The parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large spacelike momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a "color" gauge group which commutes with SU(3) \ifmmode\times\else\texttimes\fi{} SU(3). The problem of symmetry breaking is discussed. It appears likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken and that the severe infrared singularities prevent the occurrence of noncolor singlet physical states. The deep-inelastic structure functions, as well as the electron-positron total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive light-cone or parton-model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.

/pdf/asymptotically-free-gauge-theories-i-45auk8stnd.pdf

David J. Gross

Papers

Ultraviolet Behavior of Non-Abelian Gauge Theories

QCD and instantons at finite temperature

Dynamical symmetry breaking in asymptotically free field theories

Asymptotically Free Gauge Theories. I

String Theory Beyond the Planck Scale