Resurgence for large $c$ expansion in Coulomb gas formalism

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 $⟨{\varphi }_{2,1}(0){\varphi }_{2,1}(z,\bar{z}){\varphi }_{2,1}(1){\varphi }_{2,1}(\infty )⟩$, 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.

26+1 pages, 11 figures