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arXiv · hep-lat/0009036

Real Representation in Chiral Gauge Theories on the Lattice

Hiroshi Suzuki
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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.

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BibTeXRIS

Hiroshi Suzuki. 2000-12-03. Real Representation in Chiral Gauge Theories on the Lattice. https://doi.org/10.1088/1126-6708%2F2000%2F10%2F039

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