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 >= 3. We close with speculation on more general ranks of Kronecker quiver including the nonprimitive cases.