Ali Zahabi: Asymptotic BPS counting on toric quivers and Mahler measure

by Ali Zahabi (Université de Bourgogne)

First, we review the BPS sector in N = 2, four-dimensional toric quiver gauge theories and its relation to crystal melting model and dimer model. Then, we introduce the Mahler measure associated with the statistical dimer model to study the thermodynamic limit of these quiver gauge theories. In this limit, the generating function of BPS states in a general toric quiver theory is studied and entropy, growth rate of BPS states and free energy of the quiver are obtained in terms of the Mahler measure. Finally, we consider some concrete examples and present explicit computations of the profile function, entropy density, BPS growth rate and phase structure of quivers.