Puzzles for Matrix Models of Chiral Field Theories

TL;DR

This paper explores the relationship between certain chiral field theories and matrix models, revealing a necessary modification to the Dijkgraaf-Vafa conjecture due to anomaly cancellation constraints.

Contribution

It identifies a limitation in the original conjecture and proposes a modified correspondence applicable to a specific class of chiral models with matter fields.

Findings

Holomorphic matrix model is consistent only for two fundamental fields.

Original Dijkgraaf-Vafa conjecture requires modification for chiral models.

Modified correspondence remains valid despite the mismatch.

Abstract

We summarize the field-theory/matrix model correspondence for a chiral N=1 model with matter in the adjoint, antisymmetric and conjugate symmetric representations as well as eight fundamentals to cancel the chiral anomaly. The associated holomorphic matrix model is consistent only for two fundamental fields, which requires a modification of the original Dijkgraaf-Vafa conjecture. The modified correspondence holds in spite of this mismatch.