Loop equations, matrix models, and N=1 supersymmetric gauge theories

Details Loop equations, matrix models, and N=1 supersymmetric gauge theories Loop equations, matrix models, and N=1 supersymmetric gauge theories

2003-04-15

arxiv.org/abs/hep-th/0304138v3

JHEP 0305 (2003) 059

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, amstex, no figures. v2: references added. v3: minor corrections

Scientific paper

10.1088/1126-6708/2003/05/059

We derive the Konishi anomaly equations for N=1 supersymmetric gauge theories based on the classical gauge groups with matter in two-index tensor and fundamental representations, thus extending the existing results for U(N). A general formula is obtained which expresses solutions to the Konishi anomaly equation in terms of solutions to the loop equations of the corresponding matrix model. This provides an alternative to the diagrammatic proof that the perturbative part of the glueball superpotential $W_{\rm eff}$ for these matter representations can be computed from matrix model integrals, and further shows that the two approaches always give the same result. The anomaly approach is found to be computationally more efficient in the cases we studied. Also, we show in the anomaly approach how theories with a traceless two-index tensor can be solved using an associated theory with a traceful tensor and appropriately chosen coupling constants.

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