<p>We develop a resurgence analysis for large central charge (large <i>C</i>) expansions in two-dimensional CFTs using the Coulomb gas formalism. Through the exact Borel-Laplace representations of the conformal blocks <i>I</i><sub>1</sub>(<i>C, z</i>) and <i>I</i><sub>2</sub>(<i>C, z</i>) associated with the four-point correlation function <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\langle {\phi }_{2,1}\left(0\right){\phi }_{2,1}\left(z, \overline{z }\right){\phi }_{2,1}\left(1\right){\phi }_{2,1}(\infty )\rangle \)</EquationSource> </InlineEquation>, we demonstrate that <i>I</i><sub>1</sub>(<i>C, z</i>) participates in the Stokes phenomenon of <i>I</i><sub>2</sub>(<i>C, z</i>) (and vice versa), and establish that monodromy in <i>z</i> arises from alien calculus in the Borel plane variable <i>ζ</i> (Borel dual to <i>C</i>). 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.</p>

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Resurgence for large C expansion in Coulomb gas formalism

  • Yong Li,
  • Hongfei Shu

摘要

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 \(\langle {\phi }_{2,1}\left(0\right){\phi }_{2,1}\left(z, \overline{z }\right){\phi }_{2,1}\left(1\right){\phi }_{2,1}(\infty )\rangle \) , 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.