Correlation Functions In Field Theories Research Articles

Conformal field theories from deformations of theories withWnsymmetry

We construct a set of non-rational conformal field theories that consist of deformations of Toda field theory for sl(n). Besides conformal invariance, the theories still enjoy a remnant infinite-dimensional affine symmetry. The case n=3 is used to illustrate this phenomenon, together with further deformations that yield enhanced Kac-Moody symmetry algebras. For generic n we compute N-point correlation functions on the Riemann sphere and show that these can be expressed in terms of sl(n) Toda field theory correlation functions.

Graviton multipoint functions at the AdS boundary

The gauge-gravity duality can be used to relate connected multipoint graviton functions to connected multipoint correlation functions of the stress tensor of a strongly coupled fluid. Here, we show how to construct the connected graviton functions for a particular kinematic regime that is ideal for discriminating between different gravitational theories, in particular between Einstein theory and its leading-order string theory correction. Our analysis begins with the one-particle irreducible graviton amplitudes in an anti-de Sitter black brane background. We show how these can be used to calculate the connected graviton functions and demonstrate that the two types of amplitudes agree in some cases. It is then asserted on physical grounds that this agreement persists in all cases for both Einstein gravity and its leading-order correction. This outcome implies that the corresponding field-theory correlation functions can be read off directly from the bulk Lagrangian, just as can be done for the ratio of the shear viscosity to the entropy density.

Time singularities of correlators from Dirichlet conditions in AdS/CFT

Within AdS/CFT, we establish a general procedure for obtaining the leading singularity of two-point correlators involving operator insertions at different times. The procedure obtained is applied to operators dual to a scalar field which satisfies Dirichlet boundary conditions on an arbitrary time-like surface in the bulk. We determine how the Dirichlet boundary conditions influence the singularity structure of the field theory correlation functions. New singularities appear at boundary points connected by null geodesics bouncing between the Dirichlet surface and the boundary. We propose that their appearance can be interpreted as due to a non-local double trace deformation of the dual field theory, in which the two insertions of the operator are separated in time. The procedure developed in this paper provides a technical tool which may prove useful in view of describing holographic thermalization using gravitational collapse in AdS space.

On topological field theory representation of higher analogs of classical special functions

Looking for a quantum field theory model of Archimedean algebraic geometry a class of infinite-dimensional integral representations of classical special functions was introduced. Precisely the special functions such as Whittaker functions and Gamma-function were identified with correlation functions in topological field theories on a two-dimensional disk. Mirror symmetry of the underlying topological field theory leads to a dual finite-dimensional integral representations reproducing classical integral representations for the corresponding special functions. The mirror symmetry interchanging infinite- and finite-dimensional integral representations provides an incarnation of the local Archimedean Langlands duality on the level of classical special functions. In this note we provide some directions to higher-dimensional generalizations of our previous results. In the first part we consider topological field theory representations of multiple local L-factors introduced by Kurokawa and expressed through multiple Barnes's Gamma-functions. In the second part we are dealing with generalizations based on consideration of topological Yang-Mills theories on non-compact four-dimensional manifolds. Presumably, in analogy with the mirror duality in two-dimensions, S-dual description should be instrumental for deriving integral representations for a particular class of quantum field theory correlation functions and thus providing a new interesting class of special functions supplied with canonical integral representations.

Fluctuation, dissipation, and thermalization in nonequilibriumAdS5black hole geometries

We give a simple recipe for computing dissipation and fluctuations (commutator and anticommutator correlation functions) for nonequilibrium black hole geometries. The recipe formulates Hawking radiation as an initial value problem, and is suitable for numerical work. We show how to package the fluctuation and dissipation near the event horizon into correlators on the stretched horizon. These horizon correlators determine the bulk and boundary field theory correlation functions. In addition, the horizon correlators are the components of a horizon effective action, which provides a quantum generalization of the membrane paradigm. In equilibrium, the analysis reproduces previous results on the Brownian motion of a heavy quark. Out of equilibrium, Wigner transforms of commutator and anticommutator correlation functions obey a fluctuation-dissipation relation at high frequency.

AN−1conformal Toda field theory correlation functions from conformal 𝒩 = 2 SU(N) quiver gauge theories

<i>A</i>_<i>N</i>−1conformal Toda field theory correlation functions from conformal 𝒩 = 2 SU(<i>N</i>) quiver gauge theories

The space-time operator product expansion in string theory duals of field theories

We study the operator product expansion (OPE) limit of correlation functions in field theories which possess string theory duals, from the point of view of the string worldsheet. We show how the interesting (single-trace) terms in the OPE of the field theory arise in this limit from the OPE of the worldsheet theory of the string dual, using a dominant saddle point which appears in computations of worldsheet correlation functions in the space-time OPE limit. The worldsheet OPE generically contains only non-physical operators, but all the non-physical contributions are resummed by the saddle point to a contribution similar to that of a physical operator, which exactly matches the field theory expectations. We verify that the OPE limit of the worldsheet theory does not have any other contributions to the OPE limit of space-time correlation functions. Our discussion is completely general and applies to any local field theory (conformal at high energies) that has a weakly coupled string theory dual (with arbitrary curvature). As a first application, we compare our results to a proposal of R. Gopakumar for the string theory dual of free gauge theories.

Bulk-cone singularities &amp; signatures of horizon formation in AdS/CFT

We discuss the relation between singularities of correlation functions and causal properties of the bulk spacetime in the context of the AdS/CFT correspondence. In particular, we argue that the boundary field theory correlation functions are singular when the insertion points are connected causally by a bulk null geodesic. This implies the existence of "bulk-cone singularities" in boundary theory correlation functions which lie inside the boundary light-cone. We exhibit the pattern of singularities in various asymptotically AdS spacetimes and argue that this pattern can be used to probe the bulk geometry. We apply this correspondence to the specific case of shell collapse in AdS/CFT and indicate a sharp feature in the boundary observables corresponding to black hole event horizon formation.

From free fields to AdS space. I

Free $\mathcal{N}=4$ super Yang-Mills theory (in the large-N limit) is dual to an, as yet, intractable closed string theory on ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{5}.$ We aim to implement open-closed string duality in this system and thereby recast the free-field correlation functions as amplitudes in AdS space. The basic strategy is to implement this duality directly on planar field theory correlation functions in the worldline (or first quantized) formulation. The worldline loops (remnants of the worldsheet holes) close to form tree diagrams. These tree diagrams are then to be manifested as tree amplitudes in AdS space by a change of variables on the worldline moduli space (i.e., Schwinger parameter space). Restricting to twist-2 operators, we are able to carry through this program for two- and three-point functions. However, it appears that this strategy can be implemented for four- and higher-point functions as well. An analogy to electrical networks is very useful in this regard.