Degenerate operators and the 1/c expansion: Lorentzian resummations, high order computations, and super-Virasoro blocks

• Published in: The journal of high energy physics Vol. 2017; no. 3; pp. 1 - 47
• Main Authors: Chen, Hongbin, Fitzpatrick, A. Liam, Kaplan, Jared, Li, Daliang, Wang, Junpu
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2017; Springer Nature B.V; Springer Berlin; SpringerOpen
• Subjects: 1/N Expansion; AdS-CFT Correspondence; Chaos theory; Classical and Quantum Gravitation; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Classical Theories of Gravity; Computation; Conformal and W Symmetry; Conformal Field Theory; Correlators; Elementary Particles; Gauge Symmetry; Gauge-gravity correspondence; High energy physics; Lyapunov exponents; Mathematical analysis; Operators; Physics; Physics and Astronomy; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Symmetry; Texts; AdS-CFT Correspondence; Conformal and W Symmetry; Conformal Field Theory; 1/N Expansion
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP03(2017)167

A bstract One can obtain exact information about Virasoro conformal blocks by analytically continuing the correlators of degenerate operators. We argued in recent work that this technique can be used to explicitly resolve information loss problems in AdS 3 /CFT 2 . In this paper we use the technique to perform calculations in the small 1/ c ∝ G N expansion: (1) we prove the all-orders resummation of logarithmic factors ∝ 1 c log z in the Lorentzian regime, demonstrating that 1 /c corrections directly shift Lyapunov exponents associated with chaos, as claimed in prior work, (2) we perform another all-orders resummation in the limit of large c with fixed cz , interpolating between the early onset of chaos and late time behavior, (3) we explicitly compute the Virasoro vacuum block to order 1 /c 2 and 1 /c 3 with external dimensions fixed, corresponding to 2 and 3 loop calculations in AdS 3 , and (4) we derive the heavy-light vacuum blocks in theories with N = 1 , 2 superconformal symmetry.