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

TL;DR

This paper extends the derivation of Konishi anomaly equations to a broader class of N=1 supersymmetric gauge theories with various matter representations, linking them to matrix model loop equations for efficient computation of the superpotential.

Contribution

It generalizes the Konishi anomaly equations to classical gauge groups with diverse matter content and establishes a direct connection to matrix model loop equations, offering a more efficient computational approach.

Findings

Derived generalized Konishi anomaly equations for new gauge theories.

Established equivalence between anomaly and matrix model approaches for superpotential calculation.

Demonstrated computational efficiency of the anomaly method in studied cases.

Abstract

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.