The Fuzzy Ginsparg-Wilson algebra: A Solution of the fermion doubling problem - INSPIRE

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The Fuzzy Ginsparg-Wilson algebra: A Solution of the fermion doubling problem

A.P. Balachandran
(
- Syracuse U.
)
,
Giorgio Immirzi
(
- Perugia U. and
- INFN, Perugia
)

Jan, 2003

16 pages

Published in:

Phys.Rev.D 68 (2003) 065023

e-Print:

hep-th/0301242 [hep-th]

DOI:

10.1103/PhysRevD.68.065023

Report number:

SU-4252-769,
DFUP-02-14

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Abstract:

The Ginsparg-Wilson algebra is the algebra underlying the Ginsparg-Wilson solution of the fermion doubling problem in lattice gauge theory. The Dirac operator of the fuzzy sphere is not afflicted with this problem. Previously we have indicated that there is a Ginsparg-Wilson operator underlying it as well in the absence of gauge fields and instantons. Here we develop this observation systematically and establish a Dirac operator theory for the fuzzy sphere with or without gauge fields, and always with the Ginsparg-Wilson algebra. There is no fermion doubling in this theory. The association of the Ginsparg-Wilson algebra with the fuzzy sphere is surprising as the latter is not designed with this algebra in mind. The theory reproduces the integrated U(1)_A anomaly and index theory correctly.

11.30.Rd
11.15.Ha
11.10.Lm
fermion: lattice field theory
operator: algebra
gauge field theory: Yang-Mills
operator: Dirac
instanton
Ginsparg-Wilson relation
sphere: fuzzy

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Figures(0)

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