Real representation in chiral gauge theories on the lattice

DOI10.1088/1126-6708/2000/10/039zbMATH Open0965.81053arXivhep-lat/0009036OpenAlexW2144926419MaRDI QIDQ5928823

Hiroshi Suzuki

Publication date: 4 April 2001

Published in: Journal of High Energy Physics (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/hep-lat/0009036

Mathematics Subject Classification ID

Quantum field theory on lattices (81T25) String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30)

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