Deconfinement in Yang-Mills theory through toroidal compactification with deformation

Abstract

We introduce field theory techniques through which the deconfinement transition of four-dimensional Yang-Mills theory can be moved to a semi-classical domain where it becomes calculable using two-dimensional field theory. We achieve this through a double-trace deformation of toroidally compactified Yang-Mills theory onAt large N , fixed-L, and arbitrary β, the thermodynamics of the deformed theory is equivalent to that of ordinary Yang-Mills theory at leading order in the large N expansion. At fixed-N , small L and a range of β, the deformed theory maps to a two-dimensional theory with electric and magnetic (order and disorder) perturbations, analogs of which appear in planar spin-systems and statistical physics. We show that in this regime the deconfinement transition is driven by the competition between electric and magnetic perturbations in this two-dimensional theory. This appears to support the scenario proposed by Liao and Shuryak [1] regarding the magnetic component of the quark-gluon plasma at RHIC.

On the global structure of deformed Yang-Mills theory and QCD(adj) on ℝ 3 × S 1 $$ {\mathrm{\mathbb{R}}}^3\times {\mathbb{S}}^1 $$

“…We do this because the effective description of the thermal theory in the low temperature regime β L of [16] exhibits interesting duality properties, not much noted before, except for some remarks…”

“…Ref. [16] (see also the earlier work of [43] on a similar description in the Polyakov model, and also the work [44] for other perspective) argued that the thermal partition function of dYM reduces to a two-dimensional "classical" electricmagnetic Coulomb gas of W -bosons and monopole-instantons and that this gas exhibits a deconfinement phase transition at T c = g 2 4πL . Qualitatively, at low-temperatures magnetic charges (the monopole-instantons) are dominant, causing screening of magnetic charge and confinement of electric charges.…”

“…Previous work found that in the low-temperature β L regime, still at Λ QCD LN c 1, there is a thermal deconfinement transition, both in dYM [16] and QCD(adj) [17]. The effective theory near the transition is a two-dimensional Coulomb gas of electrically and magnetically charged particles.…”

“…We stress that the invariance of the long-distance action under (3.15) is exact to all loop orders (and, as we shall see below in all cases we study, nonperturbatively 16 ) despite 15 Again, we use β β β0j−1 = −β β βj−1N c , noting that every root appears squared in the derivative terms and that β β β →β β β is simply a relabeling of all the positive roots. 16 Indeed, finding the symmetry (3.16) from the nonperturbative potentials (3.23), (3.25) is quick, but it is important to realize that it is an exact symmetry to all loop orders.…”

“…16 Indeed, finding the symmetry (3.16) from the nonperturbative potentials (3.23), (3.25) is quick, but it is important to realize that it is an exact symmetry to all loop orders.…”