Moduli space of BPS walls in supersymmetric gauge theories

Norisuke Sakai, Yisong Yang

Research output: Contribution to journalArticle

Abstract

Existence and uniqueness of the solution are proved for the 'master equation' derived from the BPS equation for the vector multiplet scalar in the U(1) gauge theory with N F charged matter hypermultiplets with eight supercharges. This proof establishes that the solutions of the BPS equations are completely characterized by the moduli matrices divided by the V-equivalence relation for the gauge theory at finite gauge couplings. Therefore the moduli space at finite gauge couplings is topologically the same manifold as that at infinite gauge coupling, where the gauged linear sigma model reduces to a nonlinear sigma model. The proof is extended to the U(N C) gauge theory with N F hypermultiplets in the fundamental representation, provided the moduli matrix of the domain wall solution is U(1)-factorizable. Thus the dimension of the moduli space of U(N C) gauge theory is bounded from below by the dimension of the U(1)-factorizable part of the moduli space. We also obtain sharp estimates of the asymptotic exponential decay which depend on both the gauge coupling and the hypermultiplet mass differences.

Original languageEnglish (US)
Pages (from-to)783-800
Number of pages18
JournalCommunications in Mathematical Physics
Volume267
Issue number3
DOIs
StatePublished - Nov 2006

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Gauge Theory
Moduli Space
gauge theory
Gauge
Modulus
Nonlinear sigma Model
Sigma Models
Domain Wall
uniqueness
Master Equation
matrices
Equivalence relation
Exponential Decay
domain wall
equivalence
Linear Model
Existence and Uniqueness
fine structure
Scalar
scalars

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Moduli space of BPS walls in supersymmetric gauge theories. / Sakai, Norisuke; Yang, Yisong.

In: Communications in Mathematical Physics, Vol. 267, No. 3, 11.2006, p. 783-800.

Research output: Contribution to journalArticle

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