Admissibility Condition and Nontrivial Indices on a Noncommutative Torus

Abstract

We study the index of the Ginsparg-Wilson Dirac operator on a noncommutative torus numerically. To do this, we first formulate an admissibility condition which suppresses the fluctuation of gauge fields sufficiently small. Assuming this condition, we generate gauge configurations randomly, and find various configurations with nontrivial indices. We show one example of configurations with index 1 explicitly. This result provides the first evidence that nontrivial indices can be naturally defined on the noncommutative torus by utilizing the Ginsparg-Wilson relation and the admissibility condition.

5 pages, (v2) table 1 replaced, (v3) references added, typos corrected, the final version to appear in Phys.Rev.D

References in corpus (3)

• Describing Curved Spaces by Matrices
• Dynamical generation of a nontrivial index on the fuzzy 2-sphere
• Topology conserving gauge action and the overlap-Dirac operator

Cited by in corpus (5)

• Ginsparg-Wilson Dirac operator in the monopole backgrounds on the fuzzy 2-sphere
• The index of the overlap Dirac operator on a discretized 2d non-commutative torus
• Probability distribution of the index in gauge theory on 2d non-commutative geometry
• Index theorem in spontaneously symmetry-broken gauge theories on a fuzzy 2-sphere
• Lattice QCD with fixed topology