Yang–Mills theory in the SO(2,3)⋆ model of noncommutative gravity

Abstract

According to the standard cosmological model, thermodynamic conditions of the early Universe were such that nuclear matter existed in the state of quark–gluon plasma, rather than hadrons. On the other hand, it is generally believed that quantum gravity effects become ever more stronger as we approach the Big Bang, in particular, we expect that the phenomenon of space–time noncommutativity will be significant. Thus we are led to consider the properties of quarks and gluons in noncommutative space–time. For this, we employ the [Formula: see text] model of noncommutative gravity. As a first step towards the full theoretical treatment of the effects of noncommutativity on quark–gluon plasma, our main goal in this paper is to consistently incorporate Yang–Mills gauge fields in the [Formula: see text] framework and investigate their coupling to gravity that arises due to space–time noncommutativity. We construct an action that is invariant under deformed [Formula: see text] gauge transformations and expand it perturbatively in orders of the canonical deformation parameter [Formula: see text] via Seiberg–Witten map. In particular, we analyze the flat-space–time limit and demonstrate that residual noncommutativity induces various new couplings of quarks and gluons.