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      Large-\(N\) integrated correlators in \(\mathcal{N}=4\) SYM: when resurgence meets modularity

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          Abstract

          Exact expressions for certain integrated correlators of four half-BPS operators in \(\mathcal{N}=4\) supersymmetric Yang-Mills theory with gauge group \(SU(N)\) have been recently obtained thanks to a beautiful interplay between supersymmetric localisation and modular invariance. The large-\(N\) expansion at fixed Yang-Mills coupling of such integrated correlators produces an asymptotic series of perturbative terms, holographically related to higher derivative interactions in the low energy expansion of the type IIB effective action, as well as exponentially suppressed corrections at large \(N\), interpreted as contributions from coincident \((p,q)\)-string world-sheet instantons. In this work we define a manifestly modular invariant Borel resummation of the perturbative large-\(N\) expansion of these integrated correlators, from which we extract the exact non-perturbative large-\(N\) sectors via resurgence analysis. Furthermore, we show that in the 't Hooft limit such modular invariant non-perturbative completions reduce to known resurgent genus expansions. Finally, we clarify how the same non-perturbative data is encoded in the decomposition of the integrated correlators based on \(\rm{SL}(2,\mathbb{Z})\) spectral theory.

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          Journal
          16 May 2024
          Article
          2405.10204
          d6947762-b74e-4c5a-a1a8-6779f89adf9a

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          36 pages, 2 figures
          hep-th

          High energy & Particle physics
          High energy & Particle physics

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