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Register a new userDual formulations of vortex strings in supersymmetric Abelian Higgs model
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We discuss dual formulations of vortex strings (magnetic flux tubes) in the four-dimensional ${cal N} =1$ 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.
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Dyonic non-Abelian local/semi-global vortex strings are studied in detail in supersymmetric/non-supersymmetric Yang-Mills-Higgs theories. While the BPS tension formula is known to be the same as that for the BPS dyonic instanton, we find that the non-BPS tension formula is approximated very well by the well-known tension formula of the BPS dyon. We show that this mysterious tension formula for the dyonic non-BPS vortex stings can be understood from the perspective of a low energy effective field theory. Furthermore, we propose an efficient method to obtain an effective theory of a single vortex string, which includes not only lower derivative terms but also all order derivative corrections by making use of the tension formula. We also find a novel dyonic vortex string whose internal orientation vectors rotate in time and spiral along the string axis.
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