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We study Ihara’s 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’s zeta function to be the generating function for the generic superpotential of the gauge theory.
|Additional Information:||Electronic version of an article published as International Journal of Modern Physics A, 30(18-19), doi: 10.1142/S0217751X15501183 © World Scientific Publishing Company http://www.worldscientific.com/worldscinet/ijmpa|
|Uncontrolled Keywords:||Seiberg duality; gauge theories; Ihara’s zeta function|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||School of Engineering & Mathematical Sciences > Department of Mathematical Science|
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