Real representation in chiral gauge theories on the lattice

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3 Citations (Scopus)


The Weyl fermion belonging to the real representation of the gauge group provides a simple illustrative example for Luscher'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.

Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalJournal of High Energy Physics
Issue number10 PART B
Publication statusPublished - 2000
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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