New phases ofSU(3)andSU(4)at finite temperature

Abstract

The addition of an adjoint Polyakov loop term to the action of a pure gauge theory at finite temperature leads to new phases of SU (N ) gauge theories. For SU (3), a new phase is found which breaks Z(3) symmetry in a novel way; for SU (4), the new phase exhibits spontaneous symmetry breaking of Z(4) to Z(2), representing a partially confined phase in which quarks are confined, but diquarks are not. The overall phase structure and thermodynamics is consistent with a theoretical model of the effective potential for the Polyakov loop based on perturbation theory.

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

“…The physics of YM theory with the double trace deformation (3.1) has been studied in the continuum [11,12] (motivated in part by large-N c volume independence) and on the lattice [30]. The double-trace deformation ∆S ensures that the vacuum is at the center-symmetric point, see (3.4) below.…”

“…30 Notice that (4.5) acts as both electric-magnetic and high-T/low-T (Kramers-Wannier) duality. We stress again that we do not claim that (4.5) is a fundamental (i.e.…”

“…Nonetheless, we shall see that with respect to the global structure of the theory, (4.5) has properties common with both Kramers-Wannier duality in the Ising model and strongcharges) and co-roots α α α * i (labeling magnetic charges). 30 We note that the partition function can be cast into the form of a self-dual sin-Gordon model, whose critical features have been studied in [46]; for related works see [42,47,48].…”

Neutral bions in the ℂ $$ \mathbb{C} $$ P N −1 model

“…It is stressed byÜnsal and his collaborators that these configurations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], which are termed "bions", have two physical significances associated with two types of topologically trivial bion configurations called "magnetic (charged) bions" and "neutral bions", as seen in the following examples: in the weak-coupling regime (L ≪ 1/Λ QCD ) in QCD(adj.) on R 3 × S 1 , or in the U(1) N −1 center-symmetric phase [20][21][22][23][24][25][26][27][28][29], condensation of magnetic bions (zero topological charge and nonzero magnetic charge) causes the confinement [3][4][5][6][7][8][9]. This confinement mechanism may remain responsible for the confinement at strong-coupling regime due to the continuity principle.…”

“…The two constituents are getting closer and finally are merged by the attractive force, as shown in figure 7. The resultant configuration at τ = −∞ (λ 2 1 /λ 2 = 0) is given by 22) for N = 2, and 23) for general N , with the quantum number 24) which is identical to a trivial vacuum.…”