Supermatrix models, loop equations, and duality

Abstract

We study integrals over Hermitian supermatrices of arbitrary size $p+q$, that are parametrized by an external field $X$ and a source $Y$, of respective size $m+n$ and $p+q$. We show that these integrals exhibit a simple topological expansion in powers of a formal parameter $\hslash$, which can be identified with $1/(p-q)$. The loop equation and the associated spectral curve are also obtained. The solutions to the loop equation are given in terms of the symplectic invariants introduced in arXiv:math-ph/0702045. The symmetry property of the latter objects allows us to prove a duality that relates supermatrix models in which the role of $X$ and $Y$ are interchanged.

27 pages, 9 figures, ams latex

References in corpus (5)

• Free energy topological expansion for the 2-matrix model
• Duality in random matrix ensembles for all Beta
• Intersection theory from duality and replica
• Topological expansion of the chain of matrices
• Character expansion method for supergroups and extended superversions of the Leutwyler-Smilga and Berezin-Karpelevich integrals

Cited by in corpus (2)

• Towards U(N|M) knot invariant from ABJM theory
• Duality and integrability of supermatrix model with external source