
Physics 2009
Supermatrix models, loop equations, and dualityDOI: 10.1063/1.3430564 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 $\hbar$, which can be identified with $1/(pq)$. 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:mathph/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.
