Yang-Mills Matrix Theory

Abstract

We discuss bosonic and supersymmetric Yang-Mills matrix models with compact semi-simple gauge group. We begin by finding convergence conditions for the partition and correlation functions. Moving on, we specialise to the SU(N) models with large N. In both the Yang-Mills and cohomological formulations, we find all quantities which are invariant under the supercharges. Finally, we apply the deformation method of Moore, Nekrasov and Shatashvili directly to the Yang-Mills model. We find a deformation of the action which generates mass terms for all the matrix fields whilst preserving some supersymmetry. This allows us to rigorously integrate over a BRST quartet and arrive at the well known formula of MNS.

PhD thesis, 78 pages, reference added

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• A note on instanton counting for N=2 gauge theories with classical gauge groups
• Rotational Symmetry Breaking in Multi-Matrix Models
• On Matrix Model Formulations of Noncommutative Yang-Mills Theories
• N=4 super Yang-Mills matrix integrals for almost all simple gauge groups
• Matrix models and the gravitational interaction
• Polyakov Lines in Yang-Mills Matrix Models
• Bulk Witten Indices from D=10 Yang Mills Integrals
• Equivariant Fields in an $SU(\mathcal{N})$ Gauge Theory with new Spontaneously Generated Fuzzy Extra Dimensions
• Measure of the potential valleys of the supermembrane theory