Ginsparg-Wilson Relation, Topological Invariants and Finite Noncommutative Geometry
High Energy Physics - Theory
2009-11-07 v3 High Energy Physics - Lattice
Mathematical Physics
math.MP
Quantum Algebra
Abstract
We show that the Ginsparg-Wilson (GW) relation can play an important role to define chiral structures in {\it finite} noncommutative geometries. Employing GW relation, we can prove the index theorem and construct topological invariants even if the system has only finite degrees of freedom. As an example, we consider a gauge theory on a fuzzy two-sphere and give an explicit construction of a noncommutative analog of the GW relation, chirality operator and the index theorem. The topological invariant is shown to coincide with the 1st Chern class in the commutative limit.
Keywords
Cite
@article{arxiv.hep-th/0209223,
title = {Ginsparg-Wilson Relation, Topological Invariants and Finite Noncommutative Geometry},
author = {Hajime Aoki and Satoshi Iso and Keiichi Nagao},
journal= {arXiv preprint arXiv:hep-th/0209223},
year = {2009}
}
Comments
Revtex4 file, 5 pages, references added, typo corrected, the final version to appear in Phys.Rev.D