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New vortex-string worldsheet theories from supersymmetric localization

  • Efrat Gerchkovitz
  • Avner KarasikEmail author
Open Access
Regular Article - Theoretical Physics
  • 25 Downloads

Abstract

We use supersymmetric localization techniques to study the low-energy dynamics of BPS vortex-strings in four-dimensional \( \mathcal{N}=2 \) theories. We focus on theories with SU(Nc) × U(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 [1]. 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 \( \mathcal{N}=\left(2,2\right) \) 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.

Keywords

Extended Supersymmetry Nonperturbative Effects Solitons Monopoles and Instantons Supersymmetry and Duality 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of Particle Physics and AstrophysicsWeizmann Institute of ScienceRehovotIsrael

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