Graph Zeta Function and Gauge Theories

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.

35 pages, 7 Figures

References in corpus (7)

• D-Brane Gauge Theories from Toric Singularities and Toric Duality
• Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics
• Brane Tilings
• Brane Tilings and Their Applications
• Non-Abelian Finite Gauge Theories
• On the Classification of Brane Tilings
• Probing the Space of Toric Quiver Theories

Cited by in corpus (3)

• Eta Products, BPS States and K3 Surfaces
• Kazakov-Migdal model on the Graph and Ihara Zeta Function
• Seiberg Duality, Quiver Gauge Theories, and Ihara Zeta Function