Exact low-temperature Green's functions in AdS/CFT: From Heun to confluent Heun

Autor:	Arnaudo, Paolo, Withers, Benjamin
Rok vydání:	2024
Předmět:	High Energy Physics - Theory Condensed Matter - Strongly Correlated Electrons General Relativity and Quantum Cosmology Mathematical Physics
Druh dokumentu:	Working Paper
Popis:	We obtain exact expressions for correlation functions of charged scalar operators at finite density and low temperature in CFT$_4$ dual to the RN-AdS$_5$ black brane. We use recent developments in the Heun connection problem in black hole perturbation theory arising from Liouville CFT and the AGT correspondence. The connection problem is solved perturbatively in an instanton counting parameter, which is controlled in a double-scaling limit where $\omega, T \to 0$ holding $\omega/T$ fixed. This provides analytic control over the emergence of the zero temperature branch cut as a confluent limit of the Heun equation. From the Green's function we extract analytic results for the critical temperature of the holographic superconductor, as well as dispersion relations for both gapped and gapless low temperature quasinormal modes. We demonstrate precise agreement with numerics. Comment: 7 pages + supplemental material, 3 figures, 1 table. Comments welcome. Version 2: References added, typos fixed. Extended discussion of AdS2 results. Added further expressions for subleading terms
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.01923 Zobrazit plný text záznamu View this record from Arxiv