Topological Expansion of Oscillatory BGW and HCIZ Integrals at Strong Coupling

Abstract

We prove that the BGW and HCIZ integrals admit large N topological expansions for complex coupling and complex external fields, provided the coupling is sufficiently strong. The expansion coefficients are holomorphic functions which are genus-specific generating functions for the monotone single and double Hurwitz numbers, respectively.

arXiv comment46 pages, 1 figure. Supersedes arXiv:2006.04304v1