Solving matrix models using holomorphy

Details Solving matrix models using holomorphy Solving matrix models using holomorphy

2003-03-04

arxiv.org/abs/hep-th/0303033v1

JHEP 0306 (2003) 019

Physics

High Energy Physics

High Energy Physics - Theory

38 pages, JHEP style, 1 figure

Scientific paper

10.1088/1126-6708/2003/06/019

We investigate the relationship between supersymmetric gauge theories with moduli spaces and matrix models. Particular attention is given to situations where the moduli space gets quantum corrected. These corrections are controlled by holomorphy. It is argued that these quantum deformations give rise to non-trivial relations for generalized resolvents that must hold in the associated matrix model. These relations allow to solve a sector of the associated matrix model in a similar way to a one-matrix model, by studying a curve that encodes the generalized resolvents. At the level of loop equations for the matrix model, the situations with a moduli space can sometimes be considered as a degeneration of an infinite set of linear equations, and the quantum moduli space encodes the consistency conditions for these equations to have a solution.

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