New Vortex-String Worldsheet Theories from Supersymmetric Localization

TL;DR

This paper uses supersymmetric localization to derive two-dimensional worldsheet theories for vortex-strings in 4D N=2 theories, providing a new method to connect 4D bulk dynamics with 2D string worldsheet theories.

Contribution

It introduces a prescription to extract worldsheet two-sphere partition functions from 4D ellipsoid partition functions, linking 4D theories with 2D GLSMs and analyzing their spectra and dualities.

Findings

Derived a general formula for the worldsheet two-sphere partition function.

Identified N=(2,2) GLSMs corresponding to vortex-strings in various 4D theories.

Confirmed the spectra predictions match localization results and explored S-duality mappings.

Abstract

We use supersymmetric localization techniques to study the low-energy dynamics of BPS vortex-strings in four-dimensional N=2 theories. We focus on theories with SU(Nc)xU(1) gauge group and Nf hypermultiplets, all in the fundamental representation of SU(Nc) but with general U(1) charges. Recently, we proposed a condition that determines whether the low-energy string dynamics is captured by a two-dimensional worldsheet theory that decouples from the bulk. For strings for which this decoupling applies, we propose a prescription for extracting the two-sphere partition function of the string worldsheet theory from the four-ellipsoid partition function of the parent theory. We obtain a general formula for the worldsheet two-sphere partition function in terms of the parameters of the four-dimensional theory and identify N=(2,2) GLSMs that possess these partition functions in a large class of examples. In these examples, the weak coupling regime of the four-dimensional theory is mapped to the weak coupling regime of the worldsheet theory. In addition, we study the classical string zero-modes in flat space and obtain predictions for the worldsheet spectra, which agree with the low-energy spectra of the GLSMs obtained in the localization analysis. For Nf=2Nc=4, we discuss the map between string worldsheet theories under four-dimensional S-duality and use our prescription to study examples in which the weak coupling regime of the four-dimensional theory is mapped to the strong coupling regime of the worldsheet theory.