Moduli Space of BPS Walls in Supersymmetric Gauge Theories

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 Nf charged matter hypermultiplets with eight supercharges. This proof finally establishes the fact that the moduli space of the BPS domain wall solution is CP^(N_f-1) 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(Nc) gauge theory with Nf 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(Nc) 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.

18 pages, a reference added, two typos corrected(v2), several typos corrected, explanation of total moduli space added(v3)

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Cited by in corpus (24)

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• TASI Lectures on Solitons
• Non-Abelian Vortices on Cylinder -- Duality between vortices and walls
• Manifestly Supersymmetric Effective Lagrangians on BPS Solitons
• 1/2, 1/4 and 1/8 BPS Equations in SUSY Yang-Mills-Higgs Systems -- Field Theoretical Brane Configurations --
• Skyrmions from Instantons inside Domain Walls
• Domain Walls with Non-Abelian Clouds
• Intersecting Solitons, Amoeba and Tropical Geometry
• Dynamics of Domain Wall Networks
• Effective Action of Domain Wall Networks
• Dynamics of Strings between Walls
• Domain Wall Solitons Arising in Classical Gauge Field Theories
• Non-Abelian Gauge Field Localized on Walls with Four-Dimensional World Volume
• New BPS Objects in N=2 Supersymmetric Gauge Theories
• Maximally Non-Abelian Vortices from Self-dual Yang--Mills Fields
• Domain Wall Equations, Hessian of Superpotential, and Bogomol'nyi Bounds
• Solitons in Supersymmetric Gauge Theories: Moduli Matrix Approach
• Solitons in Supersymmetric Gauge Theories
• Non-integrability of Self-dual Yang-Mills-Higgs System
• Vacua and walls of mass-deformed Kähler nonlinear sigma models on $SO(2N)/U(N)$
• Vortices and Monopoles in a Harmonic Trap
• Domain walls with non-Abelian orientational moduli
• Domain Walls on Singularities