The Standard Model from a New Phase Transition on the Lattice

Abstract

Several years ago it was conjectured in the so-called Roma Approach, that gauge fixing is an essential ingredient in the lattice formulation of chiral gauge theories. In this paper we discuss in detail how the gauge-fixing approach may be realized. As in the usual (gauge invariant) lattice formulation, the continuum limit corresponds to a gaussian fixed point, that now controls both the transversal and the longitudinal modes of the gauge field. A key role is played by a new phase transition separating a conventional Higgs or Higgs-confinement phase, from a phase with broken rotational invariance. In the continuum limit we expect to find a scaling region, where the lattice correlators reproduce the euclidean correlation functions of the target (chiral) gauge theory, in the corresponding continuum gauge.

16 pages, revtex, one figure. Clarifications made, mainly in sections 3 and 6 that deal with the fermion action, to appear in Phys Rev D

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• Chiral Gauge Theory on Lattice with Domain Wall Fermions
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• Anti-Ferromagnetic Condensate in Yang-Mills Theory
• Running couplings in equivariantly gauge-fixed SU(N) Yang--Mills theories
• The Phase Diagram and Spectrum of Gauge-Fixed Abelian Lattice Gauge Theory
• Chiral Fermions on the Lattice through Gauge Fixing -- Perturbation Theory
• Fermion-number violation in regularizations that preserve fermion-number symmetry
• Periodic vacuum and particles in two dimensions
• Spontaneous breakdown of Lorentz symmetry in scalar QED with higher order derivatives
• Gauge fixed domain wall fermions on lattice at small Yukawa coupling
• More on Lattice BRST Invariance
• Remark on lattice BRST invariance
• Non-perturbatively gauge-fixed compact $U(1)$ lattice gauge theory
• Some conjectures looking for a NCG theory
• Tricritical points in a compact $U(1)$ lattice gauge theory at strong coupling
• SU(N) chiral gauge theories on the lattice: a quick overview
• The domain-wall model in an asymptotic-free dynamics