Recurrence relations for finite-temperature correlators via AdS2/CFT1

• Published in: The journal of high energy physics Vol. 2013; no. 12
• Main Author: Ohya, Satoshi
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-12-2013
• Subjects: Classical and Quantum Gravitation; Elementary Particles; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Relativity Theory; String Theory; AdS-CFT Correspondence; Black Holes; Conformal and W Symmetry
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP12(2013)011

A
bstract
This note is aimed at presenting a new algebraic approach to momentum-space correlators in conformal field theory. As an illustration we present a new Lie-algebraic method to compute frequency-space two-point functions for charged scalar operators of CFT
1
dual to AdS
2
black hole with constant background electric field. Our method is based on the real-time prescription of AdS/CFT correspondence, Euclideanization of AdS
2
black hole and projective unitary representations of the Lie algebra
(2,
) ⊕
(2,
). We derive novel recurrence relations for Euclidean CFT
1
two-point functions, which are exactly solvable and completely determine the frequency- and charge-dependences of two-point functions. Wick-rotating back to Lorentzian signature, we obtain retarded and advanced CFT
1
two-point functions that are consistent with the known results.