Publication : t09/163

Supermatrix models, loop equations, and duality

Desrosiers P. (Instituto Matematica y Física, Universidad de Talca, 2 Norte 685, Talca, Chile.)
Eynard B. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
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 expansions in powers of $(p-q)^2$. 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 \cite{EOFg}. 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.
Année de publication : 2010
Revue : J. Math. Phys. 51 123304 (2010)
DOI : 10.1063/1.3430564
Preprint : arXiv:0911.1762
Keywords : Matrix models, Supermatrices, Algebraic curves, Duality
Langue : Anglais

 

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