Abstract
We analyze perturbative aspects of gauged matrix models, including those where classically the gauge symmetry is partially broken. Ghost fields play a crucial role in the Feynman rules for these vacua. We use this formalism to elucidate the fact that non-perturbative aspects of N=1 gauge theories can be computed systematically using perturbative techniques of matrix models, even if we do not possess an exact solution for the matrix model. As examples we show how the Seiberg-Witten solution for N=2 gauge theory, the Montonen-Olive modular invariance for N=1*, and the superpotential for the Leigh-Strassler deformation of N=4 can be systematically computed in perturbation theory of the matrix model/gauge theory (even though in some of these cases the exact answer can also be obtained by summing up planar diagrams of matrix models).
Highlights
In this paper we study perturbative aspects of matrix models as applied to nonperturbative dynamics of N = 1 supersymmetric gauge theories in four dimensions [1,2,3]
As a byproduct of the results of this paper, which might be interesting to the matrix model specialists, we demonstrate how the matrix models with several eigenvalue supports in the large N limit can be studied by means of the planar diagram technique and established well-defined Feynman rules for it. (This subject is discussed in [15].) Another novelty which is not well explored in the matrix model literature is the possibility of filling the minima and the maxima of the matrix potential, by virtue of the analytical continuation in the filling parameters
The organization of this paper is as follows: In section 2 we show how gauge fixing in the one matrix model with the cubic potential is done, when the classical vacuum partially breaks the gauge symmetry
Summary
In some cases the planar diagrams of matrix model can be summed up exactly This gives rise to a dual geometry at the planar limit, from which one can read off nontrivial holomorphic information about the associated supersymmetric gauge theory. In this respect it is interesting to note that up to now all the cases where the supersymmetric gauge theory can be solved using strong/weak coupling dualities fall in the class of exactly soluble matrix models. As a byproduct of the results of this paper, which might be interesting to the matrix model specialists, we demonstrate how the matrix models with several eigenvalue supports in the large N limit can be studied by means of the planar diagram technique and established well-defined Feynman rules for it.
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