Asymptotics of Ground State Degeneracies in Quiver Quantum Mechanics
Abstract
We study the growth of the ground state degeneracy in the Kronecker model of quiver quantum mechanics. This is the simplest quiver with two gauge groups and bifundamental matter fields, and appears universally in the context of BPS state counting in four-dimensional N=2 systems. For large ranks, the ground state degeneracy is exponential with slope a modular function that we are able to compute at integral values of its argument. We also observe that the exponential of the slope is an algebraic number and determine its associated algebraic equation explicitly in several examples. The speed of growth of the degeneracies, together with various physical features of the bound states, suggests a dual string interpretation.
Keywords
Cite
@article{arxiv.1503.03178,
title = {Asymptotics of Ground State Degeneracies in Quiver Quantum Mechanics},
author = {Clay Cordova and Shu-Heng Shao},
journal= {arXiv preprint arXiv:1503.03178},
year = {2015}
}
Comments
30 pages, 8 figures, several large equations