Resurgence for large $c$ expansion in Coulomb gas formalism

TL;DR

This paper applies resurgence analysis to large central charge expansions in 2D CFTs using Coulomb gas formalism, revealing non-perturbative relations between conformal blocks and their monodromies.

Contribution

It introduces a resurgence framework for conformal blocks at large central charge, connecting monodromy and alien calculus to uncover non-perturbative structures.

Findings

Demonstrates Stokes phenomenon between conformal blocks

Establishes monodromy from alien calculus in Borel plane

Reveals non-perturbative connections between conformal blocks

Abstract

We develop a resurgence analysis for large central charge (large $C$) expansions in two-dimensional CFTs using the Coulomb gas formalism. Through the exact Borel-Laplace representations of the conformal blocks $I_1(C,z)$ and $I_2(C,z)$ associated with the four-point correlation function $ \langle \phi_{2,1}(0)\phi_{2,1}(z,\bar{z})\phi_{2,1}(1)\phi_{2,1}(\infty)\rangle$, we demonstrate that $I_1(C,z)$ participates in the Stokes phenomenon of $I_2(C,z)$ (and vice versa), and establish that monodromy in $z$ arises from alien calculus in the Borel plane variable $\zeta$ (Borel dual to $C$). From a given conformal block, resurgence theory thus enables us to discover other internal operators (conformal blocks). This approach establishes a non-perturbative connection between conformal blocks, shedding light on the resurgence phenomena in more general quantum field theories.