Graph Zeta Function and Gauge Theories

TL;DR

This paper explores the application of Ihara's Graph Zeta Function to analyze spectral properties of quiver gauge theories and periodic bipartite graph tilings, linking number theory with gauge theory structures.

Contribution

It introduces the use of Ihara's Graph Zeta Function to study spectral and number theoretic properties of supersymmetric gauge theories with complex vacuum manifolds.

Findings

Spectral analysis of adjacency matrices reveals insights into gauge theory properties.

Some gauge theories satisfy the graph-theoretic Riemann Hypothesis.

Connections between graph zeta functions and gauge theory vacuum structures.

Abstract

Along the recently trodden path of studying certain number theoretic properties of gauge theories, especially supersymmetric theories whose vacuum manifolds are non-trivial, we investigate Ihara's Graph Zeta Function for large classes of quiver theories and periodic tilings by bi-partite graphs. In particular, we examine issues such as the spectra of the adjacency and whether the gauge theory satisfies the strong and weak versions of the graph theoretical analogue of the Riemann Hypothesis.