Dual formulations of vortex strings in a supersymmetric Abelian Higgs model

Abstract

We discuss dual formulations of vortex strings (magnetic flux tubes) in the four-dimensional N = 1 supersymmetric Abelian Higgs model with the Fayet-Iliopoulos term in the superspace formalism. The Lagrangian of the model is dualized into a Lagrangian of the BF -type described by a chiral spinor gauge superfield including a 2-form gauge field. The dual Lagrangian is further dualized into a Lagrangian given by a chiral spinor superfield including a massive 2-form field. In both of the dual formulations, we obtain a superfield into which the vortex strings and their superpartners are embedded. We show the dual Lagrangians in terms of a superspace and a component formalism. In these dual Lagrangians, we explicitly show that the vortex strings of the original model are described by a string current electrically coupled with the 2-form gauge field or the massive 2-form field.

Topological order in the color-flavor locked phase of a ( 3+1 )-dimensional U(N) gauge-Higgs system

“…Although we have considered the U (N ) gauge group in this paper, more general gauge group of the type [U (1) × G]/C(G) would be possible [79], where C(G) denotes the center of the group G. Supersymmetric theories with topological vortices would allow us to do the analysis in a controlled way [30][31][32][33], for which the superfield formulation of duality of vortices in Ref. [80] would be useful.…”

Emergent discrete 3-form symmetry and domain walls

“…In the BF theory, a 2-form gauge field couples to the magnetic vortices [23,24] (see also Ref. [25] as a recent reference). We can see that a Wilson loop and a vortex world sheet can have a nontrivial linking phase.…”