Real-time finite-temperature correlators from AdS/CFT

Journal Article · Thu Jul 15 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.82.025019· OSTI ID:21410163

Barnes, Edwin; Vaman, Diana; Chaolun, Wu; Arnold, Peter ^[1]

---

1. Department of Physics, University of Virginia McCormick Rd, Charlottesville, Virginia 22904 (United States)

In this paper we use anti-de Sitter/conformal field theory correspondence ideas in conjunction with insights from finite-temperature real-time field theory formalism to compute 3-point correlators of N=4 super Yang-Mills operators, in real time and at finite temperature. To this end, we propose that the gravity field action is integrated only over the right and left quadrants of the Penrose diagram of the anti-de Sitter-Schwarzschild background, with a relative sign between the two terms. For concreteness we consider the case of a scalar field in the black hole background. Using the scalar field Schwinger-Keldysh bulk-to-boundary propagators, we give the general expression of a 3-point real-time Green's correlator. We then note that this particular prescription amounts to adapting the finite-temperature analog of Veltman's circling rules to tree-level Witten diagrams, and comment on the retarded and Feynman scalar bulk-to-boundary propagators. We subject our prescription to several checks: Kubo-Martin-Schwinger identities, the largest time equation, and the zero-temperature limit. When specializing to a particular retarded (causal) 3-point function, we find a very simple answer: the momentum-space correlator is given by three causal (two advanced and one retarded) bulk-to-boundary propagators, meeting at a vertex point which is integrated from spatial infinity to the horizon only. This result is expected based on analyticity, since the retarded n-point functions are obtained by analytic continuation from the imaginary-time Green's function, and based on causality considerations.

• OSTI ID: 21410163
• Journal Information: Physical Review. D, Particles Fields, Vol. 82, Issue 2; Other Information: DOI: 10.1103/PhysRevD.82.025019; (c) 2010 The American Physical Society; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANTI DE SITTER SPACE
BLACK HOLES
CAUSALITY
CONFORMAL INVARIANCE
EQUATIONS
GRAVITATION
GREEN FUNCTION
PROPAGATOR
QUANTUM FIELD THEORY
SCALAR FIELDS
SCHWARZSCHILD METRIC
YANG-MILLS THEORY
FIELD THEORIES
FUNCTIONS
INVARIANCE PRINCIPLES
MATHEMATICAL SPACE
METRICS
SPACE