Vortex-strings in N $$ \mathcal{N} $$ = 2 quiver × U(1) theories

Abstract We study 1 2 $$ \frac{1}{2} $$ -BPS vortex-strings in four dimensional N $$ \mathcal{N} $$ = 2 supersymmetric quiver theories with gauge group SU(N) n × 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 $$ \mathcal{N} $$ = (2, 2) supersymmetric non-linear sigma model. We analyze the conditions for weak→weak 2d-4d map of parameters, and identify the worldsheet theory in all the cases where the map is weak→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→strong