Chiral Lattice Gauge Theories Via Mirror-Fermion Decoupling: A Mission (im)Possible?

Abstract

This is a review of the status and outstanding issues in attempts to construct chiral lattice gauge theories by decoupling the mirror fermions from a vectorlike theory. In the first half, we explain why studying nonperturbative chiral gauge dynamics may be of interest, enumerate the problems that a lattice formulation of chiral gauge theories must overcome, and briefly review our current knowledge. We then discuss the motivation and idea of mirror-fermion decoupling and illustrate the desired features of the decoupling dynamics by a simple solvable toy model. The role of exact chiral symmetries and matching of 't Hooft anomalies on the lattice is also explained. The second, more technical, half of the article is devoted to a discussion of the known and unknown features of mirror-decoupling dynamics formulated with Ginsparg-Wilson fermions. We end by pointing out possible directions for future studies.

53 pp; 6 figs; added table of contents, references, fixed typos

References in corpus (7)

• Lectures on Supersymmetry Breaking
• Progress in four-dimensional lattice supersymmetry
• On Yang-Mills Theories with Chiral Matter at Strong Coupling
• Chiral Lattice Gauge Theories from Warped Domain Walls and Ginsparg-Wilson Fermions
• Approaching a strong fourth family
• "Light from chaos" in two dimensions
• Majorana fermions and CP-invariance of chiral gauge theories on the lattice

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