1995/06/15 by Markus A. Luty, Washington Taylor, Washington Taylor IV · 4 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Gauge group #Gauge theory #Hamiltonian lattice gauge theory #Holomorphic function #Mathematical physics #Mathematics #Moduli space #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Superpotential #Supersymmetric gauge theory #Supersymmetry #Theoretical physics #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.53.3399
published as Phys.Rev.D53:3399-3405,1996 · 14 pages, LaTeX (uses revtex.sty)
arxiv created 1995/06/15 · openalex publication_date 1996/03/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We give a simple description of the classical moduli space of vacua for supersymmetric gauge theories with or without a superpotential. The key ingredient in our analysis is the observation that the Lagrangian is invariant under the action of the complexified gauge group Gc. From this point of view the usual D-flatness conditions are an artifact of the Wess-Zumino gauge. By using a gauge that preserves Gc invariance we show that every constant matter field configuration that extremizes the superpotential is Gc gauge equivalent (in a sense that we make precise) to a unique classical vacuum. This result is used to prove that in the absence of a superpotential the classical moduli space is the algebraic variety described by the set of all holomorphic gauge-invariant polynomials. When a superpotential is present, we show that the classical moduli space is a variety defined by imposing additional relations on the holomorphic polynomials. Many of these points are already contained in the existing literature. The main contribution of the present work is that we give a careful and self-contained treatment of limit points and singularities.