Virasoro conformal blocks and thermality from classical background fields

• Published in: The journal of high energy physics Vol. 2015; no. 11; pp. 1 - 32
• Main Authors: Fitzpatrick, A. Liam, Kaplan, Jared, Walters, Matthew T.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2015; Springer Nature B.V; Springer Berlin
• Subjects: AdS-CFT correspondence; Charge; Classical and Quantum Gravitation; conformal and W Symmetry; Coupling; Elementary Particles; Equivalence; High energy physics; Operators; Physics; Physics and Astronomy; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Placing; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Recursion; Regular Article - Theoretical Physics; Relativity Theory; Seeds; Stress tensors; String Theory; AdS-CFT Correspondence; Conformal and W Symmetry
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP11(2015)200

A bstract We show that in 2d CFTs at large central charge, the coupling of the stress tensor to heavy operators can be re-absorbed by placing the CFT in a non-trivial background metric. This leads to a more precise computation of the Virasoro conformal blocks between heavy and light operators, which are shown to be equivalent to global conformal blocks evaluated in the new background. We also generalize to the case where the operators carry U(1) charges. The refined Virasoro blocks can be used as the seed for a new Virasoro block recursion relation expanded in the heavy-light limit. We comment on the implications of our results for the universality of black hole thermality in AdS 3 , or equivalently, the eigenstate thermalization hypothesis for CFT 2 at large central charge.