Equivariant Gauge Fixing of SU(2) Lattice Gauge Theory

Abstract

I construct a Lattice Gauge Theory (LGT) with discrete Z_2 structure group and an equivariant BRST symmetry that is physically equivalent to the standard SU(2)-LGT. The measure of this Z_2-LGT is invariant under all the discrete symmetries of the lattice and its partition function does not vanish. The Topological Lattice Theories (TLT) that localize on the moduli spaces are explicitly constructed and their BRST symmetry is exhibited. The ghosts of the Z_2-invariant local LGT are integrated in favor of a nonlocal bosonic measure. In addition to the SU(2) link variables and the coupling g^2, this effective bosonic measure also depends on an auxiliary gauge invariant site variable of canonical dimension two and on a gauge parameter α. The relation between the expectation value of the auxiliary field, the gauge parameter αand the lattice spacing $a$ is obtained to lowest order in the loop expansion. In four dimensions and the critical limit this expectation value is a physical scale proportional to Λ_L in the gauge α=g^2 (11-n_f)/24+ O(g^4). Implications for the loop expansion of observables in such a critical gauge are discussed.

46 pages, Latex, updated and shortened version to appear in Phys.Rev.D

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• Lattice Gauge Fixing, Gribov Copies and BRST Symmetry
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• Infrared Saturation and Phases of Gauge Theories with BRST Symmetry
• D-Brane Probes in the Matrix Model
• Curci-Ferrari mass and the Neuberger problem
• A Center-Symmetric 1/N Expansion
• Gravity and On-Shell Probe Actions
• Enumerating Copies in the First Gribov Region on the Lattice in up to four Dimensions
• Poincare' Symmetry of the GZ-Model
• Running couplings in equivariantly gauge-fixed SU(N) Yang--Mills theories
• Partial Gauge Fixing and Equivariant Cohomology
• Phase with no mass gap in non-perturbatively gauge-fixed Yang--Mills theory
• Nonperturbative Gauge Fixing and Perturbation Theory
• Non-perturbatively gauge-fixed compact $U(1)$ lattice gauge theory
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• Gauge-fixing on the Lattice via Orbifolding
• Tricritical points in a compact $U(1)$ lattice gauge theory at strong coupling
• A window on infrared QCD with small expansion parameters
• Dimensional transmutation in the longitudinal sector of equivariantly gauge-fixed Yang-Mills theory
• SU(N) chiral gauge theories on the lattice: a quick overview
• The Gribov problem and its solution from a toy model point of view
• Causal Space-Times on a Null Lattice