Quivers via anomaly chains

TL;DR

This paper develops a method using anomaly chains to derive algebraic equations constraining resolvents in quiver gauge theories, enabling calculation of operator VEVs and reproducing known RG cascade results.

Contribution

Introduces a systematic approach with anomaly chains to analyze quiver gauge theories and derive higher-order relations among resolvents.

Findings

Derived quadratic and cubic equations for resolvents in quiver theories.

Explicitly computed VEVs of chiral operators with bifundamental insertions.

Reproduced the RG cascade behavior in affine quiver theories.

Abstract

We study quivers in the context of matrix models. We introduce chains of generalized Konishi anomalies to write the quadratic and cubic equations that constrain the resolvents of general affine and non-affine quiver gauge theories, and give a procedure to calculate all higher-order relations. For these theories we also evaluate, as functions of the resolvents, VEV's of chiral operators with two and four bifundamental insertions. As an example of the general procedure we explicitly consider the two simplest quivers A2 and A1(affine), obtaining in the first case a cubic algebraic curve, and for the affine theory the same equation as that of U(N) theories with adjoint matter, successfully reproducing the RG cascade result.