Deconfinement to confinement by generalizing BRST symmetry on the sphere

TL;DR

This paper extends the finite field dependent BRST (FFBRST) technique to curved space, specifically the 4-sphere, to demonstrate a novel mechanism for phase transition between confined and deconfined phases in QCD.

Contribution

It introduces two new formulations of FFBRST transformations on curved space that induce phase transitions between confined and deconfined phases without relying on ghost condensation.

Findings

Successfully applied FFBRST on 4-sphere for phase transition

Proposed two different phase-changing transformations

Demonstrated phase change without BRST invariance

Abstract

Recently it has been shown that the theory in the quadratic gauge on 4-sphere, $\mathbb{S}^{4}$ consists of two phases namely, the confined and the deconfined phases. A suitable finite field dependent BRST (FFBRST) transformation interrelates two different gauge fixed theories. In this paper, we use the FFBRST technique on the curved space for the first time and elaborate a novel application of it. We propose two different formulations of this technique that transform the deconfined phase action on sphere to the confined phase action on sphere inside the quadratic gauge. Both proposed passages change the phase with BRST invariance to the phase without BRST invariance unlike usual connections where the FFBRST operation leave the BRST symmetry intact and there is a unique field theoretic essence of them, which makes them particularly important to study. Thus, the two different field redefinitions act as a new mechanism that execute phase transition between two real QCD phases on 4-sphere other than ghost condensation process.