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Communications in Mathematical Physics

, Volume 267, Issue 3, pp 783–800 | Cite as

Moduli Space of BPS Walls in Supersymmetric Gauge Theories

  • Norisuke SakaiEmail author
  • Yisong Yang
Article

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.

Keywords

Gauge Theory Modulus Space Domain Wall Master Equation Gauge Coupling 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of PhysicsTokyo Institute of TechnologyTokyoJapan
  2. 2.Department of MathematicsPolytechnic UniversityBrooklynU.S.A.

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