Modular-invariant large-N completion of an integrated correlator in N=4 supersymmetric Yang-Mills theory

The use of supersymmetric localisation has recently led to modular covariant expressions for certain integrated correlators of half-BPS operators in 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 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.

Automated summary

The use of supersymmetric localisation has led to modular covariant expressions for integrated correlators of half-BPS operators in N = 4 supersymmetric Yang-Mills theory with a general classical gauge group. Generating functions for such integrated correlators have been determined, confirming previously conjectured formulae. This provides a systematic understanding of the relation between properties of these correlators at finite N and their expansions at large N, including a non-perturbative completion of the large-N expansion in terms of non-holomorphic modular functions.