The index of the overlap Dirac operator on a discretized 2 d non-commutative torus

@inproceedings{Aoki2007TheIO,
title={The index of the overlap Dirac operator on a discretized 2 d non-commutative torus},
author={Hajime Aoki and Jun -Ichi Nishimura and Yoshiaki Susaki},
year={2007}
}

The index, which is given in terms of the number of zero modes of the Dirac operator with definite chirality, plays a central role in various topological aspects of gauge theories. We investigate its properties in non-commutative geometry. As a simple example, we consider the U(1) gauge theory on a discretized 2d non-commutative torus, in which general classical solutions are known. For such backgrounds we calculate the index of the overlap Dirac operator satisfying the Ginsparg-Wilson relation… CONTINUE READING