Scaling Behaviour of Quiver Quantum Mechanics

Understand

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.