### Abstract

We investigate the structure of the moduli space of multiple BPS non-Abelian vortices in U(N) gauge theory with N fundamental Higgs fields, focusing our attention on the action of the exact global (color-flavor diagonal) SU(N) symmetry on it. The moduli space of a single non-Abelian vortex, ℂP ^{N-1}, is spanned by a vector in the fundamental representation of the global SU(N) symmetry. The moduli space of winding-number k vortices is instead spanned by vectors in the direct-product representation: they decompose into the sum of irreducible representations each of which is associated with a Young tableau made of k boxes, in a way somewhat similar to the standard group composition rule of SU(N) multiplets. The Kähler potential is exactly determined in each moduli subspace, corresponding to an irreducible SU(N) orbit of the highest-weight configuration.

Original language | English |
---|---|

Article number | 042 |

Journal | Journal of High Energy Physics |

Volume | 2010 |

Issue number | 11 |

DOIs | |

Publication status | Published - 2010 |

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### Keywords

- Confinement
- Duality in gauge field theories
- Nonperturbative effects
- Solitons monopoles and instantons

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2010*(11), [042]. https://doi.org/10.1007/JHEP11(2010)042

**Group theory of non-Abelian vortices.** / Eto, Minoru; Fujimori, Toshiaki; Gudnason, Sven Bjarke; Jiang, Yunguo; Konishi, Kenichi; Nitta, Muneto; Ohashi, Keisuke.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2010, no. 11, 042. https://doi.org/10.1007/JHEP11(2010)042

}

TY - JOUR

T1 - Group theory of non-Abelian vortices

AU - Eto, Minoru

AU - Fujimori, Toshiaki

AU - Gudnason, Sven Bjarke

AU - Jiang, Yunguo

AU - Konishi, Kenichi

AU - Nitta, Muneto

AU - Ohashi, Keisuke

PY - 2010

Y1 - 2010

N2 - We investigate the structure of the moduli space of multiple BPS non-Abelian vortices in U(N) gauge theory with N fundamental Higgs fields, focusing our attention on the action of the exact global (color-flavor diagonal) SU(N) symmetry on it. The moduli space of a single non-Abelian vortex, ℂP N-1, is spanned by a vector in the fundamental representation of the global SU(N) symmetry. The moduli space of winding-number k vortices is instead spanned by vectors in the direct-product representation: they decompose into the sum of irreducible representations each of which is associated with a Young tableau made of k boxes, in a way somewhat similar to the standard group composition rule of SU(N) multiplets. The Kähler potential is exactly determined in each moduli subspace, corresponding to an irreducible SU(N) orbit of the highest-weight configuration.

AB - We investigate the structure of the moduli space of multiple BPS non-Abelian vortices in U(N) gauge theory with N fundamental Higgs fields, focusing our attention on the action of the exact global (color-flavor diagonal) SU(N) symmetry on it. The moduli space of a single non-Abelian vortex, ℂP N-1, is spanned by a vector in the fundamental representation of the global SU(N) symmetry. The moduli space of winding-number k vortices is instead spanned by vectors in the direct-product representation: they decompose into the sum of irreducible representations each of which is associated with a Young tableau made of k boxes, in a way somewhat similar to the standard group composition rule of SU(N) multiplets. The Kähler potential is exactly determined in each moduli subspace, corresponding to an irreducible SU(N) orbit of the highest-weight configuration.

KW - Confinement

KW - Duality in gauge field theories

KW - Nonperturbative effects

KW - Solitons monopoles and instantons

UR - http://www.scopus.com/inward/record.url?scp=78649709235&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78649709235&partnerID=8YFLogxK

U2 - 10.1007/JHEP11(2010)042

DO - 10.1007/JHEP11(2010)042

M3 - Article

VL - 2010

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 11

M1 - 042

ER -