Finite Temperature Deconfining Transition in the BRST Formalism

We present a toy model study of the high temperature deconfining transition in Yang-Mills theory as a breakdown of the confinement condition proposed by Kugo and Ojima. Our toy model is a kind of topological field theory obtained from the Yang-Mills theory by taking the limit of vanishing gauge coupling constant $g_{\rm YM}\to 0$, and therefore the gauge field $A_\mu$ is constrained to the pure-gauge configuration $A_\mu=g^{\dagger}\partial_\mu g$. At zero temperature this model has been known to satisfy the confinement condition of Kugo and Ojima which requires the absence of the massless Nambu-Goldstone-like mode coupled to the BRST-exact color current. In the finite temperature case based on the real-time formalism, our model in 3+1 dimensions is reduced, by the Parisi-Sourlas mechanism, to the ``sum'' of chiral models in 1+1 dimensions with various boundary conditions of the group element $g(t,x)$ at the ends of the time contour. We analyze the effective potential of the $SU(2)$ model and find that the deconfining transition in fact occurs due to the contribution of the sectors with non-periodic boundary conditions.