Exceptional thermodynamics: the equation of state of G2 gauge theory

Abstract

We present a lattice study of the equation of state in Yang-Mills theory based on the exceptional G 2 gauge group. As is well-known, at zero temperature this theory shares many qualitative features with real-world QCD, including the absence of colored states in the spectrum and dynamical string breaking at large distances. In agreement with previous works, we show that at finite temperature this theory features a first-order deconfining phase transition, whose nature can be studied by a semi-classical computation. We also show that the equilibrium thermodynamic observables in the deconfined phase bear striking quantitative similarities with those found in SU(N ) gauge theories: in particular, these quantities exhibit nearly perfect proportionality to the number of gluon degrees of freedom, and the trace anomaly reveals a characteristic quadratic dependence on the temperature, also observed in SU(N ) Yang-Mills theories (both in four and in three spacetime dimensions). We compare our lattice data with analytical predictions from effective models, and discuss their implications for the deconfinement mechanism and high-temperature properties of strongly interacting, non-supersymmetric gauge theories. Our results give strong evidence for the conjecture that the thermal deconfining transition is governed by a universal mechanism, common to all simple gauge groups.

The SUSY Yang–Mills plasma in a T-matrix approach

“…Such a result is in agreement with the recent lattice study [5] showing that the SU(N) and G 2 normalized EoS are indeed compatible above T c .…”

“…First, there still exists a firstorder deconfining phase transition with the gauge groups G 2 , SU(N > 3), SP (2) and E 7 [2][3][4]. Second, the equation of state (EoS) above the deconfining temperature T c , appears to be nearly independent of the gauge group once normalized to the Stefan-Boltzmann pressure [4][5][6]. Below T c , the EoS seems to be compatible with a Hagedorn-type density of state with the Hagedorn temperature T h playing the role of T c [7,8].…”

Topology and θ dependence in finite temperature G 2 lattice gauge theory

“…The values of T /T c have been estimated by using the parametrization reported in [22] for the string tension and the following values of the critical couplings: β c (N t = 6) = 1.3951(2) (see [16]) and β c (N t = 8) = 1.431(3) (compatible with the one reported in [22]). …”

“…before string breaking [20]) satisfies Casimir scaling [13,18,20], a first order deconfinement transition is present [14,16,22], (quenched) chiral symmetry is broken in the low temperature phase and restored above the critical temperature [19], the topological susceptibility is suppressed above deconfinement [21], propagators [17] and thermodynamical observables (like e.g. pressure and trace anomaly) [22] do not show any qualitative difference with respect to the SU(N ) case.…”

“…Bearing all this in mind, it is not surprising that the G 2 lattice gauge theory was actively investigated in the past, both at zero and finite temperature [11][12][13][14][15][16][17][18][19][20][21][22]. What is probably surprising is that the results of these analysis gave a picture much similar to that of standard SU(N ) theory: the spectrum of the G 2 theory at zero temperature is composed only of color neutral objects [11,12,15], the string tension at intermediate distances (i.e.…”