A ladder of topologically non-trivial non-BPS states

TL;DR

This paper explores a quiver gauge theory on a Kähler manifold, revealing a ladder of topologically non-trivial, non-BPS states with equidistant energy levels, expanding understanding of non-BPS solutions.

Contribution

It introduces a semi-explicit construction of topologically non-trivial, non-BPS states in a quiver gauge theory, highlighting their energy spectrum and topological properties.

Findings

Identification of two energy gaps in the theory.

Existence of a ladder of non-BPS states with non-trivial topology.

States are at equidistant energy levels.

Abstract

We consider a simple quiver gauge theory with gauge group U(r1) x U(r2) and a Higgs field in the bi-fundamental representation. The back-ground for this theory is a compact K\"ahler manifold M. For a careful but natural choice of Higgs field potential the second order field equations can be replaced with a set of first order BPS equations. We show that the theory admits two energy gaps: The vacuum is topologically trivial but has finite, non-zero energy and is not a BPS state. The second gap lies between the vacuum and the first BPS state. In this gap we find a ladder of states with non-trivial topology, at equidistant energy levels. We give a semi-explicit construction for such topologically non-trivial non-BPS states.