Lattice Chiral Gauge Theories

Abstract

I review the substantial progress which has been made recently with the non-perturbative construction of chiral gauge theories on the lattice. In particular, I discuss three different approaches: a gauge invariant method using fermions which satisfy the Ginsparg-Wilson relation, and two gauge non-invariant methods, one using different cutoffs for the fermions and the gauge fields, and one using gauge fixing. Open problems within all three approaches are addressed.

15 pages, 2 figs, Lattice 2000 (Plenary)

References in corpus (7)

• Weyl fermions on the lattice and the non-abelian gauge anomaly
• Lattice regularization of chiral gauge theories to all orders of perturbation theory
• Anomaly Cancellation Condition in Lattice Gauge Theory
• Axial Anomaly in Lattice Abelian Gauge Theory in Arbitrary Dimensions
• Non-commutative Differential Calculus and the Axial Anomaly in Abelian Lattice Gauge Theories
• Global Anomalies in chiral gauge theories on the lattice
• Global obstructions to gauge-invariance in chiral gauge theory on the lattice

Cited by in corpus (38)

• Lattice tests of beyond Standard Model dynamics
• Dynamical overlap fermions, results with hybrid Monte-Carlo algorithm
• Reliability of lattice gauge theories
• Observations on staggered fermions at non-zero lattice spacing
• Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries
• Chiral Lattice Gauge Theories Via Mirror-Fermion Decoupling: A Mission (im)Possible?
• Top quark induced effective potential in a composite Higgs model
• Nonperturbative Regulator for Chiral Gauge Theories?
• On Yang-Mills Theories with Chiral Matter at Strong Coupling
• SU(N) chiral gauge theories on the lattice
• Chiral Lattice Gauge Theories and The Strong Coupling Dynamics of a Yukawa-Higgs Model with Ginsparg-Wilson Fermions
• Some Exact Results in Chiral Gauge Theories
• Chiral Lattice Gauge Theories from Warped Domain Walls and Ginsparg-Wilson Fermions
• On the decoupling of mirror fermions
• Analysis of the DeltaI=1/2 Rule and e'/e with Overlap Fermions
• A Chiral Solution to the Ginsparg-Wilson Equation
• CP breaking in lattice chiral gauge theories
• Lattice chirality and the decoupling of mirror fermions
• On the gauge invariant path-integral measure for the overlap Weyl fermions in $\underline{16}$ of SO(10)
• Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
• More chiral operators on the lattice
• Vacuum alignment and lattice artifacts: Wilson fermions
• "Light from chaos" in two dimensions
• Running couplings in equivariantly gauge-fixed SU(N) Yang--Mills theories
• Fermion-number violation in regularizations that preserve fermion-number symmetry
• Domain wall fermion and CP symmetry breaking
• Calculation of the One W Loop $H\to \gamma \gamma$ Decay Amplitude with a Lattice Regulator
• Anomaly cancellation condition in an effective non-perturbative electroweak theory
• Dynamical Gauge Symmetry Breaking in Strongly Coupled Lattice Theories
• Effective Lagrangian for strongly coupled domain wall fermions
• A renormalisation group derivation of the overlap formulation
• Symmetries of Ginsparg-Wilson Chiral Fermions
• Lattice chirality, anomaly matching, and more on the (non)decoupling of mirror fermions
• Anomalous gauge theories revisited
• Masslessness of ghosts in equivariantly gauge-fixed Yang--Mills theories
• Dimensional transmutation in the longitudinal sector of equivariantly gauge-fixed Yang-Mills theory
• Two-dimensional gauge anomalies and $p$-adic numbers
• The staggered domain wall fermion method