Degenerate Operators and the $1/c$ Expansion: Lorentzian Resummations, High Order Computations, and Super-Virasoro Blocks

Understand

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 $1/c \propto G_N$ 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 $1/c^3$, corresponding to $2$ and $3$ loop calculations in AdS$_3$, and (4) we derive the heavy-light vacuum blocks in theories with $\mathcal{N}=1,2$ superconformal symmetry.