Non-Abelian Flux Tubes in SQCD: Supersizing World-Sheet Supersymmetry

TL;DR

This paper investigates non-Abelian flux tubes in a deformed supersymmetric gauge theory, revealing that their world-sheet dynamics preserve extended supersymmetry under certain conditions, with supersymmetry breaking occurring at large deformation parameters.

Contribution

It demonstrates that non-Abelian BPS strings maintain four supercharges on the world sheet across a range of parameters, and introduces the concept of supersymmetry emergence at flux-tube junctions.

Findings

Non-Abelian BPS strings exist for all deformation parameters.

The world-sheet CP(1) model retains four supercharges in a wide parameter region.

Supersymmetry breaks down at large deformation parameters.

Abstract

We consider non-Abelian 1/2 BPS flux tubes (strings) in a deformed N=2 supersymmetric gauge theory, with mass terms mu_{1,2} of the adjoint fields breaking N=2 down to N=1. The main feature of the non-Abelian strings is the occurrence of orientational moduli associated with the possibility of rotations of their color fluxes inside a global SU(N) group. The bulk four-dimensional theory has four supercharges; half-criticality of the non-Abelian strings would imply then N=1 supersymmetry on the world sheet, i.e. two supercharges. In fact, superalgebra of the reduced moduli space has four supercharges. Internal dynamics of the orientational moduli are described by two-dimensional CP(N-1) model on the string world sheet. We focus mainly on the SU(2) case, i.e. CP(1) world-sheet theory. We show that non-Abelian BPS strings exist for all values of mu_{1,2}. The low-energy theory of moduli is indeed CP(1), with four supercharges, in a wide region of breaking parameters mu_{1,2}. Only in the limit of very large mu_{1,2}, above some critical value, the N=2 world-sheet supersymmetry breaks down to N=1. We observe "supersymmetry emergence" for the flux-tube junction (confined monopole): the "kink-monopole" is half-critical considered from the standpoint of the world-sheet CP(1) model (i.e. two supercharges conserved), while in the bulk N=1 theory there is no monopole central charge at all.