More on lattice BRST invariance

Abstract

In the gauge-fixing approach to ͑chiral͒ lattice gauge theories, the action in the U͑1͒ case implicitly contains a free ghost term, in accordance with the continuum Abelian theory. On the lattice there is no BRST symmetry and, without fermions, the partition function is strictly positive. Recently, Neuberger pointed out, Phys. Rev. D 58, 057502 ͑1998͒, that a different choice of the ghost term would lead to a BRST-invariant lattice model, which is ill defined nonperturbatively. We show that such a lattice model is inconsistent already in perturbation theory, and clearly different from the gauge-fixing approach. ͓S0556-2821͑98͒08719-0͔

Gauge-fixing approach to lattice chiral gauge theories, part II

“…For more details on φ , including a numerical computation, see [7,12]. This result leads to a very important conclusion: the full U(1) L ×U(1) R symmetry of eq.…”

“…From the dip at p 4 ∼ 0 we learn that the LH neutral fermion is not free. For m 2 = 0, explicit one-loop results [13] show that there is only a cut, and no isolated pole at p = 0, which can precisely be explained by the fact that ψ n L = φ † ψ c L only excites multi-"particle" states (of course, θ-excitations are not physically healthy particles). Similar numerical and perturbative results have been obtained for the charged propagator [7,13], which also confirm our claims about the fermion spectrum discussed here.…”

“…We conclude that one recovers a massless gauge field by tuning κ to a critical value (which beyond tree level is not equal to zero [12]). The appearance of a phase transition to this unusual phase is just a consequence of working with a regulator that breaks gauge invariance.…”

“…Here we describe the other approach, based on gauge fixing. For related work at this conference, see [6]; for more details on our approach, see [7].…”

Lattice Chiral Gauge Theories Through Gauge Fixing

“…(In a confining theory, the "chiral quarks" do not appear in the spectrum, but we may first consider the theory with only the φ dynamical, with external smooth transverse gauge fields; the "reduced model" of refs. [11,12,13].) It turns out that three things can happen (see ref.…”