Nonperturbative Regulator for Chiral Gauge Theories?

Abstract

We propose a nonperturbative gauge invariant regulator for d-dimensional chiral gauge theories on the lattice. The method involves simulating domain wall fermions in d + 1 dimensions with quantum gauge fields that reside on one d-dimensional surface and are extended into the bulk via gradient flow. The result is a theory of gauged fermions plus mirror fermions, where the mirror fermions couple to the gauge fields via a form factor that becomes exponentially soft with the separation between domain walls. The resultant theory has a local d-dimensional interpretation only if the chiral fermion representation is anomaly free. A physical realization of this construction would imply the existence of mirror fermions in the standard model that are invisible except for interactions induced by vacuum topology, and which could gravitate differently than conventional matter.

5 pages. Updated to match the published version

References in corpus (4)

• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Infinite N phase transitions in continuum Wilson loop operators
• Interacting Topological Insulator and Emergent Grand Unified Theory
• Lattice chirality and the decoupling of mirror fermions

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• Chiral Lattice Fermions From Staggered Fields
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• Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
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• Fractional quantum Hall effect in a relativistic field theory
• Fermion number anomaly with the fluffy mirror fermion
• Axial U(1) current in Grabowska and Kaplan's formulation
• Six-dimensional regularization of chiral gauge theories
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• Lattice Regularization of Reduced Kähler-Dirac Fermions and Connections to Chiral Fermions
• One-loop perturbative coupling of $A$ and $A_{\star }$ through the chiral overlap operator
• Testing the mechanism of lepton compositness
• On the infinite gradient-flow for the domain-wall formulation of chiral lattice gauge theories
• Nonperturbative renormalization of the lattice Sommerfield vector model
• Two-dimensional gauge anomalies and $p$-adic numbers
• QCD and High Energy Interactions: Moriond 2016 Theory Summary
• A calculation of the gauge anomaly with the chiral overlap operator
• Six-dimensional regularization of chiral gauge theories on a lattice