Gribov copies, BRST-exactness and Chern-Simons theory

Abstract

The path integral approach for a 3D Chern-Simons theory is discussed with a focus on the question of metric independence and BRST-exactness in the light of Gribov ambiguity. Copies of the vacuum satisfying the strong boundary conditions and with trivial winding number are shown to exist. This problem is relevant for Yang-Mills theory in 2+1 dimensions as well. Furthermore, it is also shown that there are regular background metrics supporting an infinite number of zero modes of the Abelian Faddeev-Popov operator in the Coulomb gauge. In order to avoid overcounting one could restrict the possible metrics which enter in the gauge fixing but this would imply that, at a quantum level, three-dimensional Chern-Simons theories do depend on the metric.

arXiv comment14 pages

References in corpus (8)

• The Black Hole in Three Dimensional Space Time
• Introduction to the Gribov Ambiguities In Euclidean Yang-Mills Theories
• Kontsevich Integral for Vassiliev Invariants from Chern-Simons Perturbation Theory in the Light-Cone Gauge
• Gribov pendulum in the Coulomb gauge on curved spaces
• Gravitationally induced zero modes of the Faddeev-Popov operator in the Coulomb gauge for Abelian gauge theories
• Gribov ambiguity in asymptotically AdS three-dimensional gravity
• Vassiliev Invariants in the Context of Chern-Simons Gauge Theory
• Kauffman Knot Invariant from SO(N) or Sp(N) Chern-Simons theory and the Potts Model