Resurgence for large c expansion in Coulomb gas formalism

2025/08/26 by Li, Yong, Shu, Hongfei
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2508.19059

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 I₁(C,z) and I₂(C,z) associated with the four-point correlation function ⟨ ϕ_2,1(0)ϕ_2,1(z,z)ϕ_2,1(1)ϕ_2,1(∞)⟩, we demonstrate that I₁(C,z) participates in the Stokes phenomenon of I₂(C,z) (and vice versa), and establish that monodromy in z arises from alien calculus in the Borel plane variable ζ (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.

Citations

• On the 1/c expansion in 2d CFTs with degenerate operators
• Resurgence in Liouville Theory
• Liouville conformal blocks and Stokes phenomena
• On the Moyal Star Product of Resurgent Series
• Lectures on non‐perturbative effects in large N gauge theories, matrix models and strings
• The Large N Limit of Superconformal Field Theories and Supergravity
• A new approach to solving the cubic: Cardan’s solution revealed

Related

• c_{\rm eff} from Resurgence at the Stokes Line
• On the 1/c expansion in 2d CFTs with degenerate operators
• Classical conformal blocks, Coulomb gas integrals, and quantum integrable models
• Emergent descriptions at large charge: A foray into the structure of conformal field theories and beyond
• Lectures on Resurgence in Integrable Field Theories