Regge Trajectories in $\mathcal{N}=2$ Supersymmetric Yang-Mills Theory

TL;DR

This paper shows that $ ext{N}=2$ supersymmetric Yang-Mills theories contain BPS particles forming Regge trajectories, with a novel estimation of their slope using quiver quantum mechanics, and establishes new structure theorems for moduli spaces.

Contribution

It introduces the existence of Regge trajectories in $ ext{N}=2$ supersymmetric gauge theories and provides a method to estimate their slopes through quiver quantum mechanics.

Findings

BPS particles in $ ext{N}=2$ theories obey Regge relations.

Estimated slopes of Regge trajectories for $SU(N)$ theories.

Proved structure theorems for quiver moduli spaces.

Abstract

We demonstrate that $\mathcal{N}=2$ supersymmetric non-Abelian gauge theories have towers of BPS particles obeying a Regge relation, $J \sim m^{2},$ between their angular momenta, $J,$ and their masses, $m$. For $SU(N)$ Yang-Mills theories, we estimate the slope of these Regge trajectories using a non-relativistic quiver quantum mechanics model. Along the way, we also prove various structure theorems for the quiver moduli spaces that appear in the calculation.