Real Representation in Chiral Gauge Theories on the Lattice

Abstract

The Weyl fermion belonging to the real representation of the gauge group provides a simple illustrative example for Lüscher's gauge-invariant lattice formulation of chiral gauge theories. We can explicitly construct the fermion integration measure globally over the gauge-field configuration space in the arbitrary topological sector; there is no global obstruction corresponding to the Witten anomaly. It is shown that this Weyl formulation is equivalent to a lattice formulation based on the Majorana (left--right-symmetric) fermion, in which the fermion partition function is given by the Pfaffian with a definite sign, up to physically irrelevant contact terms. This observation suggests a natural relative normalization of the fermion measure in different topological sectors for the Weyl fermion belonging to the complex representation.

uses phyzzx.tex and phyzzx.plus, 18 pages. The final version to appear in JHEP

References in corpus (5)

• Weyl fermions on the lattice and the non-abelian gauge anomaly
• Anomaly Cancellation Condition in Lattice Gauge Theory
• Gauge anomaly cancellations in SU(2)_L \times U(1)_Y Electroweak theory on the lattice
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