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
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