Exact thermal correlators of holographic $CFT$s

Abstract

We compute the exact retarded Green's functions in thermal $CFT$s with chemical potential and angular momenta using holography respectively. We consider the field equations satisfied by the quasi-normal modes in both charged and rotating black holes in $AdS$ spacetime and mapped them to the Heun equations by appropriate changes of variables. The AGT correspondence allows us to find the connection formulae among the solutions of the Heun equations near different singularities by using the crossing relations of the five-point correlators in the Liouville $CFT$. The connection formulae associated with the boundary conditions imposed on the bulk field equations yield the exact thermal correlators in the boundary $CFT$.

arXiv comment15+1 pages, minor changes and clarifications, references added, matches version to be published in JHEP

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• Holographic Thermal Correlators for Hyperbolic $CFT$s
• Absorption cross section in gravity's rainbow from confluent Heun equation
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• Holographic thermal propagator for arbitrary scale dimensions
• Finite Temperature at Finite Places
• Quantum Mechanics from General Relativity and the Quantum Friedmann Equation
• 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