Existence of multiple vortices in supersymmetric gauge field theory

Shouxin Chen, Yisong Yang

Research output: Contribution to journalArticle

Abstract

Two sharp existence and uniqueness theorems are presented for solutions of multiple vortices arising in a six-dimensional brane-world supersymmetric gauge field theory under the general gauge symmetry group G =U(1) × SU(N) and with N Higgs scalar fields in the fundamental representation of G. Specifically, when the space of extra dimension is compact so that vortices are hosted in a 2-torus of volume /ω/, the existence of a unique multiple vortex solution representing n1, . . . , nN , respectively, prescribed vortices arising in the N species of the Higgs fields is established under the explicitly stated necessary and sufficient condition ni <g2v2/8πN/ ω/ + 1/N(1 -1/N) [g/e]2)n, i =1, . . . ,N, where e and g are the U(1) electromagnetic and SU(N) chromatic coupling constants, v measures the energy scale of broken symmetry and n =σ N i=1 ni is the total vortex number; when the space of extra dimension is the full plane, the existence and uniqueness of an arbitrarily prescribed n-vortex solution of finite energy is always ensured. These vortices are governed by a system of nonlinear elliptic equations, which may be reformulated to allow a variational structure. Proofs of existence are then developed using the methods of calculus of variations.

Original languageEnglish (US)
Pages (from-to)3923-3946
Number of pages24
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume468
Issue number2148
DOIs
StatePublished - Dec 8 2012

Fingerprint

Gauge Field Theories
Gages
Vortex
Vortex flow
vortices
Extra Dimensions
Higgs
existence theorems
uniqueness theorem
calculus of variations
Brane World
Gauge Symmetry
Existence and Uniqueness Theorem
Nonlinear Elliptic Equations
Gauge Group
Calculus of variations
uniqueness
Symmetry Group
Energy
Scalar Field

Keywords

  • Calculus of variations
  • Non-Abelian gauge theory
  • Nonlinear elliptic equations
  • Vortices

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

Cite this

Existence of multiple vortices in supersymmetric gauge field theory. / Chen, Shouxin; Yang, Yisong.

In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 468, No. 2148, 08.12.2012, p. 3923-3946.

Research output: Contribution to journalArticle

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