Vortex-Strings in N=2 SQCD and Bulk-String Decoupling

TL;DR

This paper investigates the conditions under which vortex-strings in N=2 supersymmetric gauge theories decouple from bulk excitations, revealing a criterion based on charge differences and Aharonov-Bohm phases, supported by classical and non-perturbative analyses.

Contribution

It introduces a simple criterion for bulk-string decoupling in N=2 SQCD, linking it to charge differences and Aharonov-Bohm phases, with derivations from classical and supersymmetric localization methods.

Findings

Decoupling occurs when charge difference products are integer multiples of 2π.

Non-decoupling is associated with long-range zero-modes that decay slower than 1/r.

The decoupling condition matches trivial Aharonov-Bohm phase criteria.

Abstract

We study vortex-strings in four-dimensional N=2 supersymmetric SU(Nc)xU(1) gauge theories with Nf hypermultiplets in the fundamental representation of SU(Nc) and general U(1) charges. If Nf>Nc, the vacuum is not gapped and the low-energy theory contains both the vacuum massless excitations and the string zero-modes. The question we address in this work is whether the vacuum and the string moduli decouple at low energies, allowing a description of the low-energy dynamics in terms of a two-dimensional theory on the string worldsheet. We find a simple condition controlling the bulk-string coupling: If there exist two flavors such that the product of their U(1) charge difference with the magnetic flux carried by the string configuration is not an integer multiple of 2\pi, the string has zero-modes that decay slower than 1/r, where r is the radial distance from the string core. These modes are coupled to the vacuum massless excitations even at low energies. If, however, all such products are integer multiples of 2\pi, long-range modes of this type do not exist and the string moduli decouple from the bulk at low energies. This condition turns out to coincide with the condition of trivial Aharonov-Bohm phases for the particles in the spectrum. In addition to a derivation of the bulk-string decoupling criterion using classical analysis of the string zero-modes, we provide a non-perturbative derivation of the criterion, which uses supersymmetric localization techniques.