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arXiv · 2106.15483

The moduli space of non-Abelian vortices in Yang-Mills-Chern-Simons-Higgs theory

Sven Bjarke Gudnason·Minoru Eto
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Abstract

We determine the dimension of the moduli space of non-Abelian vortices in Yang-Mills-Chern-Simons-Higgs theory in 2+1 dimensions for gauge groups $G=({\rm U}(1)\times G')/\mathbb{Z}_{n_0}$ with $G'$ being an arbitrary semi-simple group and $n_0$ the greatest common divisor of the Abelian charges of the $G'$ invariants. The calculation is carried out using a Callias-type index theorem, the moduli matrix approach and a D-brane setup in Type IIB string theory. We prove that the index theorem gives the number of zeromodes or moduli of the non-Abelian vortices, extend the moduli matrix approach to the Yang-Mills-Chern-Simons-Higgs theory and finally derive the effective Lagrangian of Collie and Tong using string theory.

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Sven Bjarke Gudnason, Minoru Eto. 2021-06-29. The moduli space of non-Abelian vortices in Yang-Mills-Chern-Simons-Higgs theory. https://doi.org/10.1088/1751-8121%2Fac254b

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