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arXiv · 2210.14038

Modular-invariant large-$N$ completion of an integrated correlator in $\mathcal{N}=4$ supersymmetric Yang-Mills theory

Daniele Dorigoni·Michael B. Green·Congkao Wen·Haitian Xie
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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 $G_N$. Here we determine generating functions that encode such integrated correlators for any classical gauge group and provide a proof of previous 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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Daniele Dorigoni, Michael B. Green, Congkao Wen, Haitian Xie. 2022-10-25. Modular-invariant large-$N$ completion of an integrated correlator in $\mathcal{N}=4$ supersymmetric Yang-Mills theory. https://doi.org/10.1007/jhep04(2023)114

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