Scaling behaviour of quiver quantum mechanics

A bstract 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.