Holographic Thermal Correlators for Hyperbolic $CFT$s

Abstract

We use holography to compute the exact form of retarded Green's functions for a scalar operator with conformal dimension $\Delta$ in a thermal CFT and in its related counterpart with chemical potential in $R^1\times H^3$. In our analysis, we recast the wave equation of a scalar field in the normal form of Heun's equation in the dual gravity theories described by the AdS hyperbolic blackhole and its charged version. Heun's equation is identified to the semiclassical limit of the BPZ equation for a five-point correlator with one degenerate field insertion in the Liouville theory on the Riemann sphere. The crossing symmetry of conformal block in the Liouville theory eventually gives rise to a set of connection formulas among the solutions of Heun's equation evaluated at different regular singularities. We use the connection formula to reproduce the leading order behaviors of the scalar field near the horizon as well as near the boundary and achieve the exact form of the retarded thermal Green's function. We show a recipe to obtain the exact retarded Green's function for a thermal CFT dual to AdS blackbrane from a high-temperature limit accompanied by a complex mapping on AdS hyperbolic blackhole. Moreover, we show the retarded Green's function for the boundary CFT of Rindler AdS spacetime admits a free integer parameter.

arXiv comment17 pages, 7 tables, references added, matches the version published in JHEP

References in corpus (42)

• Gauge Theory Correlators from Non-Critical String Theory
• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Shear viscosity of strongly coupled N=4 supersymmetric Yang-Mills plasma
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Towards a derivation of holographic entanglement entropy
• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Conformal Four Point Functions and the Operator Product Expansion
• Conformal Partial Waves and the Operator Product Expansion
• Bulk vs. Boundary Dynamics in Anti-de Sitter Spacetime
• Topological Black Holes in Anti-de Sitter Space
• Holographic Probes of Anti-de Sitter Spacetimes
• Loop and surface operators in N=2 gauge theory and Liouville modular geometry
• Instantons and recursion relations in N=2 Susy gauge theory
• Quantization of Integrable Systems and Four Dimensional Gauge Theories
• Holographic Calculations of Renyi Entropy
• AdS/CFT Duals of Topological Black Holes and the Entropy of Zero-Energy States
• On geodesic propagators and black hole holography
• Black hole scrambling from hydrodynamics
• Many-body chaos and energy dynamics in holography
• Heun Functions and Some of Their Applications in Physics
• Deformed Prepotential, Quantum Integrable System and Liouville Field Theory
• Irregular Liouville correlators and connection formulae for Heun functions
• What Do CFTs Tell Us About Anti-de Sitter Spacetimes?
• Scrambling in Hyperbolic Black Holes: shock waves and pole-skipping
• Holographic thermal correlators from supersymmetric instantons
• AdS Membranes Wrapped on Surfaces of Arbitrary Genus
• Thermodynamics and Stability of Hyperbolic Charged Black Holes
• Asymptotic form of quasi-normal modes of large AdS black holes
• Correlation functions in finite temperature CFT and black hole singularities
• Perturbative connection formulas for Heun equations
• Signature of the black hole phase transition in quasinormal modes
• Scalar quasinormal modes of Kerr-AdS${}_5$
• Holographic Correlators at Finite Temperature
• Supersymmetric Rényi entropy and charged hyperbolic black holes
• On the Absorption by Near-Extremal Black Branes
• Rindler-AdS/CFT
• Exact thermal correlators of holographic $CFT$s
• Thermal one point functions, large $d$ and interior geometry of black holes
• Holographic correlation functions at finite density and/or finite temperature
• Holographic teleportation in higher dimensions
• The topological RN-AdS black holes cannot be overcharged by the new version of gedanken experiment

Cited by in corpus (6)

• Quasinormal Modes of C-metric from SCFTs
• Thermal Product Formula for Shear Modes
• Finite Temperature at Finite Places
• Holographic thermal correlators from recursions
• Notes on Quasinormal Modes of charged de Sitter Blackholes from Quiver Gauge Theories
• Connection formulae in the Collision Limit I: Case Studies in Lifshitz Geometry