Finite temperature Z(N) phase transition with Kaluza–Klein gauge fields

Abstract

If SU(N) gauge fields live in a world with a circular extra dimension, coupling there only to adjointly charged matter, the system possesses a global Z(N) symmetry. If the radius is small enough such that dimensional reduction takes place, this symmetry is spontaneously broken. It turns out that its fate at high temperatures is not easily decided with straightforward perturbation theory. Utilising non-perturbative lattice simulations, we demonstrate here that the symmetry does get restored at a certain temperature T c , both for a 3+1 and a 4+1 dimensional world (the latter with a finite cutoff). To avoid a cosmological domain wall problem, such models would thus be allowed only if the reheating temperature after inflation is below T c . We also comment on the robustness of this phenomenon with respect to small modifications of the model.

Searching for continuous phase transitions in 5D SU(2) lattice gauge theory

“…In addition, the paper [11] proposes that such a fixed point can be found in the IR limit of an RG flow starting from a known superconformal field theory, see also [12]. On the other hand, attempts to directly find and study this theory using lattice models have so-far been inconclusive [13,14], see also [15][16][17][18][19][20][21] for exploration with a compact dimension and [22] for non-Lorentz invariant extensions.…”

Radion assisted gauge inflation

“…and this estimate is supported by lattice simulations [12]. For the problem at hand however, this temperature is far above the Planck scale and so does not make much sense.…”

Renormalizable extra-dimensional models

“…continuum limit, in more than four space-time dimensions [23]. With few exceptions since then [24][25][26][27][28][29][30][31] this possibility seems to have been ignored or forgotten. Independently in string theory, probably related supersymmetric versions have been discovered [32].…”