Abstract
The use of supersymmetric localisation has recently led to modular covariant expressions for certain integrated correlators of half-BPS operators in \( \mathcal{N} \) = 4 supersymmetric Yang-Mills theory with a general classical gauge group GN. Here we determine generating functions that encode such integrated correlators for any classical gauge group and provide a proof of previously conjectured formulae. This gives a systematic understanding of the relation between properties of these correlators at finite N and their expansions at large N. In particular, it determines a duality-invariant non-perturbative completion of the large-N expansion in terms of a sum of novel non-holomorphic modular functions. These functions are exponentially suppressed at large N and have the form of a sum of contributions from coincident (p, q)-string world-sheet instantons.
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Dorigoni, D., Green, M.B., Wen, C. et al. Modular-invariant large-N completion of an integrated correlator in \( \mathcal{N} \) = 4 supersymmetric Yang-Mills theory. J. High Energ. Phys. 2023, 114 (2023). https://doi.org/10.1007/JHEP04(2023)114
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DOI: https://doi.org/10.1007/JHEP04(2023)114