Seiberg Duality, Quiver Gauge Theories, and Ihara Zeta Function

TL;DR

This paper explores the Ihara zeta function in the context of quiver gauge theories, analyzing pole distributions under Seiberg duality and proposing a refined zeta function related to superpotentials.

Contribution

It introduces a refined Ihara zeta function for quiver gauge theories and studies its properties under Seiberg duality transformations.

Findings

Pole distributions follow specific patterns along the duality tree

Refined zeta function encodes superpotential data

Connections to Riemann Hypothesis variants in graph theory

Abstract

We study Ihara zeta function for graphs in the context of quivers arising from gauge theories, especially under Seiberg duality transformations. The distribution of poles is studied as we proceed along the duality tree, in light of the weak and strong graph versions of the Riemann Hypothesis. As a by-product, we find a refined version of Ihara zeta function to be the generating function for the generic superpotential of the gauge theory.