Real representation in chiral gauge theories on the lattice | Zendy

Hiroshi Suzuki | Zendy

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Real representation in chiral gauge theories on the lattice

Author(s) -

Hiroshi Suzuki

Publication year - 2000

Publication title -

journal of high energy physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.998

H-Index - 261

eISSN - 1126-6708

pISSN - 1029-8479

DOI - 10.1088/1126-6708/2000/10/039

Subject(s) - fermion , physics , pfaffian , chiral anomaly , gauge anomaly , gauge theory , theoretical physics , majorana fermion , lattice gauge theory , real representation , gauge group , hamiltonian lattice gauge theory , quantum mechanics , majorana , mathematics , pure mathematics , irreducible representation

The Weyl fermion belonging to the real representation of the gauge groupprovides a simple illustrative example for L\"uscher's gauge-invariant latticeformulation of chiral gauge theories. We can explicitly construct the fermionintegration measure globally over the gauge-field configuration space in thearbitrary topological sector; there is no global obstruction corresponding tothe Witten anomaly. It is shown that this Weyl formulation is equivalent to alattice formulation based on the Majorana (left--right-symmetric) fermion, inwhich the fermion partition function is given by the Pfaffian with a definitesign, up to physically irrelevant contact terms. This observation suggests anatural relative normalization of the fermion measure in different topologicalsectors for the Weyl fermion belonging to the complex representation.Comment: uses phyzzx.tex and phyzzx.plus, 18 pages. The final version to appear in JHE

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