### Abstract

When instantons are put into the Higgs phase, vortices are attached to instantons. We construct such composite solitons as 1/4 BPS states in five-dimensional supersymmetric U(NC) gauge theory with NF(≥NC) fundamental hypermultiplets. We solve the hypermultiplet BPS equation and show that all 1/4 BPS solutions are generated by an NC×NF matrix which is holomorphic in two complex variables, assuming the vector multiplet BPS equation does not give additional moduli. We determine the total moduli space formed by topological sectors patched together and work out the multi-instanton solution inside a single vortex with complete moduli. Small instanton singularities are interpreted as small sigma-model lump singularities inside the vortex. The relation between monopoles and instantons in the Higgs phase is also clarified as limits of calorons in the Higgs phase. Another type of instantons stuck at an intersection of two vortices and dyonic instantons in the Higgs phase are also discussed.

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

Article number | 025011 |

Pages (from-to) | 1-19 |

Number of pages | 19 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 72 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2005 Jul 15 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Mathematical Physics

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*72*(2), 1-19. [025011]. https://doi.org/10.1103/PhysRevD.72.025011

**Instantons in the Higgs phase.** / Eto, Minoru; Isozumi, Youichi; Nitta, Muneto; Ohashi, Keisuke; Sakai, Norisuke.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 72, no. 2, 025011, pp. 1-19. https://doi.org/10.1103/PhysRevD.72.025011

}

TY - JOUR

T1 - Instantons in the Higgs phase

AU - Eto, Minoru

AU - Isozumi, Youichi

AU - Nitta, Muneto

AU - Ohashi, Keisuke

AU - Sakai, Norisuke

PY - 2005/7/15

Y1 - 2005/7/15

N2 - When instantons are put into the Higgs phase, vortices are attached to instantons. We construct such composite solitons as 1/4 BPS states in five-dimensional supersymmetric U(NC) gauge theory with NF(≥NC) fundamental hypermultiplets. We solve the hypermultiplet BPS equation and show that all 1/4 BPS solutions are generated by an NC×NF matrix which is holomorphic in two complex variables, assuming the vector multiplet BPS equation does not give additional moduli. We determine the total moduli space formed by topological sectors patched together and work out the multi-instanton solution inside a single vortex with complete moduli. Small instanton singularities are interpreted as small sigma-model lump singularities inside the vortex. The relation between monopoles and instantons in the Higgs phase is also clarified as limits of calorons in the Higgs phase. Another type of instantons stuck at an intersection of two vortices and dyonic instantons in the Higgs phase are also discussed.

AB - When instantons are put into the Higgs phase, vortices are attached to instantons. We construct such composite solitons as 1/4 BPS states in five-dimensional supersymmetric U(NC) gauge theory with NF(≥NC) fundamental hypermultiplets. We solve the hypermultiplet BPS equation and show that all 1/4 BPS solutions are generated by an NC×NF matrix which is holomorphic in two complex variables, assuming the vector multiplet BPS equation does not give additional moduli. We determine the total moduli space formed by topological sectors patched together and work out the multi-instanton solution inside a single vortex with complete moduli. Small instanton singularities are interpreted as small sigma-model lump singularities inside the vortex. The relation between monopoles and instantons in the Higgs phase is also clarified as limits of calorons in the Higgs phase. Another type of instantons stuck at an intersection of two vortices and dyonic instantons in the Higgs phase are also discussed.

UR - http://www.scopus.com/inward/record.url?scp=33749159380&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevD.72.025011

DO - 10.1103/PhysRevD.72.025011

M3 - Article

VL - 72

SP - 1

EP - 19

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 2

M1 - 025011

ER -