A lattice formulation of chiral gauge theories

Abstract

We present a method for formulating gauge theories of chiral fermions in lattice field theory. The method makes use of a Wilson mass to remove doublers. Gauge invariance is then restored by modifying the theory in two ways: the magnitude of the fermion determinant is replaced with the square root of the determinant for a fermion with vector-like couplings to the gauge field; a double limit is taken, in which the lattice spacing associated with the fermion field is sent to zero before the lattice spacing associated with the gauge field.The method applies only to theories whose fermions are in an anomaly-free representation of the gauge group. We also present a related technique for computing matrix elements of operators involving fermion fields. Although the analyses of these methods are couched in weak-coupling perturbation theory, it is argued that the computational prescriptions are gauge invariant in the presence of a nonperturbative gauge-field configuration.

Lattice chiral gauge theories

“…For a different suggestion, see ref. [54]. In fourdimensional non-abelian gauge theories a similar problem occurs, because Π 3 (G) = 0 for any nonabelian group G.…”

A Wilson-Majorana regularization for lattice chiral gauge theories

“…The problem of finding a nonperturbative formulation of a chiral gauge theory is still an active field of investigation [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. The root of this difficulty lies in the impossibility of finding a regularization procedure which preserves the chiral symmetry of the classical action functional.…”