Instantons in the Higgs phase

Minoru Eto, Youichi Isozumi, Muneto Nitta, Keisuke Ohashi, Norisuke Sakai

Research output: Contribution to journalArticle

107 Citations (Scopus)

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 languageEnglish
Article number025011
Pages (from-to)1-19
Number of pages19
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Volume72
Issue number2
DOIs
Publication statusPublished - 2005 Jul 15
Externally publishedYes

Fingerprint

Instantons
instantons
Higgs
Vortex
vortices
Modulus
Singularity
complex variables
Sigma Models
Monopole
Complex Variables
Gauge Theory
monopoles
Moduli Space
intersections
gauge theory
Solitons
Sector
sectors
solitary waves

ASJC Scopus subject areas

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

Cite this

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

In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 72, No. 2, 025011, 15.07.2005, p. 1-19.

Research output: Contribution to journalArticle

Eto, Minoru ; Isozumi, Youichi ; Nitta, Muneto ; Ohashi, Keisuke ; Sakai, Norisuke. / Instantons in the Higgs phase. In: Physical Review D - Particles, Fields, Gravitation and Cosmology. 2005 ; Vol. 72, No. 2. pp. 1-19.
@article{2cdf5be4dfe049f1b4ccb378d9559c3a,
title = "Instantons in the Higgs phase",
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.",
author = "Minoru Eto and Youichi Isozumi and Muneto Nitta and Keisuke Ohashi and Norisuke Sakai",
year = "2005",
month = "7",
day = "15",
doi = "10.1103/PhysRevD.72.025011",
language = "English",
volume = "72",
pages = "1--19",
journal = "Physical review D: Particles and fields",
issn = "1550-7998",
publisher = "American Institute of Physics",
number = "2",

}

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

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

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 -