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

Abstract

In this work we study the topological properties of the G 2 lattice gauge theory by means of Monte Carlo simulations. We focus on the behaviour of topological quantities across the deconfinement transition and investigate observables related to the θ dependence of the free energy. As in SU(N ) gauge theories, an abrupt change happens at deconfinement and an instanton gas behaviour rapidly sets in for T > T c .

Axion phenomenology and θ-dependence from N f = 2 + 1 lattice QCD

“…(3.12) with d 2 independent of T . SU(N ) and G 2 , see [14,15]) the asymptotic value is approached from below, while in the present case it is approached from above. These peculiar features can be related to a different interaction between instantons mediated by light quarks, as it is clear from the following discussion.…”

“…While data clearly approach the dilute instanton gas prediction b DIGA 2 = −1/12 at high temperature, deviations from this value are clearly visible on all the lattice spacings for T 1.3 T c and, for the smallest lattice spacing, also up to T ∼ 2.5 T c . This is in striking contrast to what is observed in pure gauge theory, where deviations from −1/12 are practically absent for T 1.15 T c , with a precision higher than 10% [13][14][15][16]. As discussed in the introduction deviations from b DIGA 2 cannot be simply ascribed to a failure of perturbation theory (like e.g.…”

“…With respect to the pure gauge case, the convergence of b 2 to DIGA is slower and the deviation is opposite in sign [14,15]. This suggests a different interaction between instantons right above T c , namely repulsive in the quenched case and attractive in full QCD [76].…”

“…[14], and later confirmed in refs. [13,15,16], that the form of the free energy in eq. (1.7) describes with high precision the physics of the system for T 1.15 T c , while for T T c everything is basically independent of the temperature, thus strengthening the conclusion χ(T < T c ) ≈ χ(T = 0) obtained in previous studies [17][18][19][20][21].…”

Exceptional thermodynamics: the equation of state of G2 gauge theory

“…This leaves only G 2 , F 4 and E 8 as compact simply-connected Lie groups with a trivial center; of these, G 2 , with rank two and dimension 14, is the smallest and hence the most suitable for a lattice Monte Carlo study. In fact, numerical simulations of this Yang-Mills theory have already been going on for some years [74][75][76][77][78][79][80][81][82][83][84][85]. Besides numerical studies, these peculiar features of G 2 Yang-Mills theory have also triggered analytical interest [86][87][88][89][90][91][92][93][94][95][96][97].…”