Chiral field theories, Konishi anomalies and matrix models

TL;DR

This paper explores the relationship between chiral N=1 U(N) gauge theories and matrix models, revealing limitations and modifications needed for theories with net chirality, and comparing chiral and nonchiral models.

Contribution

It analyzes the Konishi anomalies and loop equations in a specific chiral gauge theory, showing the matrix model correspondence requires adjustments for chiral theories.

Findings

Matrix model well-defined only for two flavors

Loop equations match Konishi constraints in 1/N expansion

Chiral theory matches nonchiral SO(N) model superpotential

Abstract

We study a chiral N=1, U(N) field theory in the context of the Dijkgraaf-Vafa correspondence. Our model contains one adjoint, one conjugate symmetric and one antisymmetric chiral multiplet, as well as eight fundamentals. We compute the generalized Konishi anomalies and compare the chiral ring relations they induce with the loop equations of the (intrinsically holomorphic) matrix model defined by the tree-level superpotential of the field theory. Surprisingly, we find that the matrix model is well-defined only if the number of flavors equals two! Despite this mismatch, we show that the 1/N expansion of the loop equations agrees with the generalized Konishi constraints. This indicates that the matrix model - gauge theory correspondence should generally be modified when applied to theories with net chirality. We also show that this chiral theory produces the same gaugino superpotential as a nonchiral SO(N) model with a single symmetric multiplet and a polynomial superpotential.