Counting Trees in Supersymmetric Quantum Mechanics
arXiv:1502.08050
Abstract
We study the supersymmetric ground states of the Kronecker model of quiver quantum mechanics. This is the simplest quiver with two gauge groups and bifundamental matter fields, and appears universally in four-dimensional N=2 systems. The ground state degeneracy may be written as a multi-dimensional contour integral, and the enumeration of poles can be simply phrased as counting bipartite trees. We solve this combinatorics problem, thereby obtaining exact formulas for the degeneracies of an infinite class of models. We also develop an algorithm to compute the angular momentum of the ground states, and present explicit expressions for the refined indices of theories where one rank is small.
50 pages, 20 figures, + appendices. v2 typos corrected, color issues in figures fixed
References in corpus (7)
- Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
- Witten Index and Wall Crossing
- Wall-Crossing from Boltzmann Black Hole Halos
- An Index Formula for Supersymmetric Quantum Mechanics
- General instanton counting and 5d SCFT
- Geometric engineering of (framed) BPS states
- About the Absence of Exotics and the Coulomb Branch Formula