Asymptotics of Ground State Degeneracies in Quiver Quantum Mechanics
arXiv:1503.03178
Abstract
We study the growth of the ground state degeneracy in the Kronecker model of quiver quantum mechanics. This is the simplest quiver with two gauge groups and bifundamental matter fields, and appears universally in the context of BPS state counting in four-dimensional N=2 systems. For large ranks, the ground state degeneracy is exponential with slope a modular function that we are able to compute at integral values of its argument. We also observe that the exponential of the slope is an algebraic number and determine its associated algebraic equation explicitly in several examples. The speed of growth of the degeneracies, together with various physical features of the bound states, suggests a dual string interpretation.
arXiv comment30 pages, 8 figures, several large equations
References in corpus (18)
- Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
- Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
- Wall-crossing, Hitchin Systems, and the WKB Approximation
- The spectrum of BPS branes on a noncompact Calabi-Yau
- Witten Index and Wall Crossing
- N=2 Quantum Field Theories and Their BPS Quivers
- BPS Quivers and Spectra of Complete N=2 Quantum Field Theories
- Cohomology of quiver moduli, functional equations, and integrality of Donaldson-Thomas type invariants
- BPS states and algebras from quivers
- From Black Holes to Quivers
- Wild Wall Crossing and BPS Giants
- An Index Formula for Supersymmetric Quantum Mechanics
- Half--Hypers and Quivers
- General instanton counting and 5d SCFT
- Geometric engineering of (framed) BPS states
- Regge Trajectories in Supersymmetric Yang-Mills Theory
- Counting Trees in Supersymmetric Quantum Mechanics
- Quivers, curves, and the tropical vertex