Scaling Behaviour of Quiver Quantum Mechanics

Abstract

We explore vacuum degeneracy of Kronecker quiver with large ranks, by computing Witten index of corresponding 1d gauged linear sigma model. For $(d-1,d{)}_k$ quivers with the intersection number $k$, we actually counted index of its mutation equivalent, $(d,(k-1)d+1{)}_k$, and find exponentially large behaviour whenever $k\ge 3$. We close with speculation on more general ranks of Kronecker quiver including the nonprimitive cases.

28 pages, 5 figures, minor typo corrected