A Chiral Solution to the Ginsparg-Wilson Equation

Abstract

We present a chiral solution of the Ginsparg-Wilson equation. This work is motivated by our recent proposal for nonperturbatively regulating chiral gauge theories, where five-dimensional domain wall fermions couple to a four-dimensional gauge field that is extended into the extra dimension as the solution to a gradient flow equation. Mirror fermions at the far surface decouple from the gauge field as if they have form factors that become infinitely soft as the distance between the two surfaces is increased. In the limit of an infinite extra dimension we derive an effective four-dimensional chiral overlap operator which is shown to obey the Ginsparg-Wilson equation, and which correctly reproduces a number of properties expected of chiral gauge theories in the continuum.

arXiv commentRevised discussions of the index, topology conservation by the gradient flow, and adiabatic versus abrupt flow. 13 pages, 2 figures

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Cited by in corpus (13)

• Axial gravity, massless fermions and trace anomalies
• Some Exact Results in Chiral Gauge Theories
• Axial gravity: a non-perturbative approach to split anomalies
• 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
• Fractional quantum Hall effect in a relativistic field theory
• Axial U(1) current in Grabowska and Kaplan's formulation
• One-loop perturbative coupling of $A$ and $A_{\star }$ through the chiral overlap operator
• On the infinite gradient-flow for the domain-wall formulation of chiral lattice gauge theories
• Six-dimensional regularization of chiral gauge theories on a lattice
• A calculation of the gauge anomaly with the chiral overlap operator
• A model of quark and lepton compositeness
• From spin models to lattice QCD -- the scientific legacy of Peter Hasenfratz