Vortex-strings in N=2 quiver X U(1) theories

TL;DR

This paper investigates half-BPS vortex-strings in four-dimensional N=2 supersymmetric quiver theories, classifying vacua, analyzing string zero modes, and exploring the conditions for bulk-string decoupling and the resulting worldsheet theories, including dualities.

Contribution

It introduces a tetris diagram for analyzing Higgs vacua, classifies vacua with FI terms, and studies the low-energy worldsheet theories, including dualities and parameter mappings in N=2 quiver theories.

Findings

Classification of vacua using tetris diagrams

Identification of worldsheet theories in weak-weak parameter regimes

Application of S-duality to relate weakly and strongly coupled worldsheet theories

Abstract

We study half-BPS vortex-strings in four dimensional N=2 supersymmetric quiver theories with gauge group SU(N)^n X U(1). The matter content of the quiver can be represented by what we call a tetris diagram, which simplifies the analysis of the Higgs vacua and the corresponding strings. We classify the vacua of these theories in the presence of a Fayet-Iliopoulos term, and study strings above fully-Higgsed vacua. The strings are studied using classical zero modes analysis, supersymmetric localization and, in some cases, also S-duality. We analyze the conditions for bulk-string decoupling at low energies. When the conditions are satisfied, the low energy theory living on the string's worldsheet is some 2d N=(2,2) supersymmetric non-linear sigma model. We analyze the conditions for weak to weak 2d-4d map of parameters, and identify the worldsheet theory in all the cases where the map is weak to weak. For some SU(2) quivers, S-duality can be used to map weakly coupled worldsheet theories to strongly coupled ones. In these cases, we are able to identify the worldsheet theories also when the 2d-4d map of parameters is weak to strong.