Real Representation in Chiral Gauge Theories on the Lattice

Details Real Representation in Chiral Gauge Theories on the Lattice Real Representation in Chiral Gauge Theories on the Lattice

2000-09-27

arxiv.org/abs/hep-lat/0009036v4

JHEP 0010 (2000) 039

Physics

High Energy Physics

High Energy Physics - Lattice

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

Scientific paper

10.1088/1126-6708/2000/10/039

The Weyl fermion belonging to the real representation of the gauge group provides a simple illustrative example for L\"uscher'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.

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