On a Z_3-Graded Generalization of the Witten Index

Details On a Z_3-Graded Generalization of the Witten Index On a Z_3-Graded Generalization of the Witten Index

2001-12-10

arxiv.org/abs/hep-th/0112069v1

Nucl.Phys. B624 (2002) 500-508

Physics

High Energy Physics

High Energy Physics - Theory

Accepted for publication in Nucl. Phys. B

Scientific paper

10.1016/S0550-3213(01)00630-7

We construct a realization of the algebra of the Z_3-graded topological symmetry of type (1,1,1) in terms of a pair of operators D_1: H_1 -> H_2, and D_2: H_2 -> H_3 satisfying [D_1D_1^\dagger,D_2^\dagger D_2]=0. We show that the sequence of the restriction of these operators to the zero-energy subspace forms a complex and establish the equality of the corresponding topological invariants with the analytic indices of these operators.

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