2024/12/05 by Agnese Bissi, Nicola Dondi, Bissi, Agnese +7 · 4 citations
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Holomorphic and Operator Theory #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2412.04387
openalex publication_date 2024/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analytically determine the large central charge asymptotic expansion of the Virasoro conformal blocks entering in four-point functions with external degenerate operators on a sphere in 2d CFTs, and study its resurgence properties as a function of the conformal cross-ratio z. We focus on the cases of four heavy (2,1) degenerate operators, and two (2,1) heavy degenerate ones plus two arbitrary light operators. The 1/c asymptotic series is Borel summable for generic values of z, but it jumps when a Stokes line is crossed. Starting from the 1/c series of the identity block, we show how a resurgent analysis allows us to completely determine the other Virasoro block and in fact to reconstruct the full correlator. We also show that forbidden singularities, known to exist in correlators with two heavy and two light operators, appear with four heavy operators as well. In both cases, they are turning points emanating Stokes lines, artefacts of the asymptotic expansion, and we show how they are non perturbatively resolved. More general correlators and implications for gravitational theories in AdS3 are briefly discussed. Our results are based on new asymptotic expansions for large parameters (a,b,c) of certain hypergeometric functions 2 F1(a,b,c;z) which can be useful in general.