On a Z3-Graded Generalization of the Witten Index
Abstract
We construct a realization of the algebra of the Z3-graded topological symmetry of type (1,1,1) in terms of a pair of operators D1: H1 -> H2, and D2: H2 -> H3 satisfying [D1D1,D2 D2]=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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