On Low Rank Classical Groups in String Theory, Gauge Theory and Matrix Models

TL;DR

This paper investigates the role of low-rank classical groups in string theory, gauge theory, and matrix models, clarifying when certain superfields should be included or set to zero, and explaining discrepancies between different approaches.

Contribution

It provides a detailed analysis of gauge group breaking patterns and the conditions for including glueball superfields, reconciling string theory, matrix models, and gauge theory results.

Findings

String theory results align with matrix models under specific conditions.

Residual instanton effects can cause discrepancies but often cancel out.

Clarifies when glueball superfields should be extremized or set to zero.

Abstract

We consider N=1 supersymmetric U(N), SO(N), and Sp(N) gauge theories, with two-index tensor matter and added tree-level superpotential, for general breaking patterns of the gauge group. By considering the string theory realization and geometric transitions, we clarify when glueball superfields should be included and extremized, or rather set to zero; this issue arises for unbroken group factors of low rank. The string theory results, which are equivalent to those of the matrix model, refer to a particular UV completion of the gauge theory, which could differ from conventional gauge theory results by residual instanton effects. Often, however, these effects exhibit miraculous cancellations, and the string theory or matrix model results end up agreeing with standard gauge theory. In particular, these string theory considerations explain and remove some apparent discrepancies between gauge theories and matrix models in the literature.