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

Abstract

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 AdS3/CFT2. 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 $$ \propto \frac{1}{c} \log\;z $$ 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 AdS3, and (4) we derive the heavy-light vacuum blocks in theories with $$ \mathcal{N} $$ = 1, 2 superconformal symmetry.