Novel phase in SU(3) lattice gauge theory with 12 light fermions

Abstract

We study the phase structure of SU(3) lattice gauge theory with N f = 12 staggered fermions in the fundamental representation, for both zero and finite temperature at strong gauge couplings. For small fermion masses we find two transitions at finite temperature that converge to two wellseparated bulk phase transitions. The phase between the two transitions appears to be a novel phase. We identify order parameters showing that the single-site shift symmetry of staggered fermions is spontaneously broken in this phase. We investigate the eigenvalue spectrum of the Dirac operator, the static potential and the meson spectrum, which collectively establish that this novel phase is confining but chirally symmetric. The phase is bordered by first-order phase transitions, and since we find the same phase structure with N f = 8 fermions, we argue that the novel phase is most likely a strong-coupling lattice artifact, the existence of which does not imply IR conformality.

Conformal finite size scaling of twelve fermion flavors

“…A similar phase structure has been observed independently by three different groups [4,9,12]. The newfound order parameter of broken shift symmetry in the intermediate phase is an interesting additional development in the study of the esoteric intermediate phase when HYP smearing is used in the staggered fermion action [9]. The intermediate phase only exists in a finite interval of the lattice gauge coupling for small enough fermion masses, as schematically sketched in Figure 1.…”

“…Our physics simulations and conformal FSS hypothesis tests were done well inside the weak coupling phase at β = 2.2 without influence from the intermediate phase, as indicated in Figure 1. A similar phase structure has been observed independently by three different groups [4,9,12]. The newfound order parameter of broken shift symmetry in the intermediate phase is an interesting additional development in the study of the esoteric intermediate phase when HYP smearing is used in the staggered fermion action [9].…”

“…Three distinct regions emerge at fixed volume and fixed fermion mass showing strong coupling behavior for β < 1.4 with a large chiral condensate, an intermediate phase for 1.4 < β < 1.8 with a sudden drop in ψψ , and a weak coupling phase for β > 1.8 with a further drop in ψψ . We also observed another distinct feature of the intermediate phase (first seen in [9]) where the pion correlator exhibits oscillations associated with the appearance of a non-degenerate parity partner state. This structure does not exist in the weak coupling phase.…”

“…Based on axial U(1) symmetry considerations, arguments were presented in [12] in favor of conformal symmetry in the weak coupling phase. This argument was criticized in [9] based on new details of the broken shift symmetry with chiral symmetry restoration they discovered at zero temperature in the bulk intermediate phase.…”

“…The frequently discussed model of twelve fermions in the fundamental representation of the SU(3) color gauge group remains controversial with continuing recent efforts from several lattice investigations [1][2][3][4][5][6][7][8][9][10][11][12][13] where more extended references can be found for the earlier history of the model. The focus of these lattice studies is to establish conformality or chiral symmetry breaking in the bulk phase close to the continuum limit.…”