Spectrum and q-index of the super q-deformed Dirac operator on the superquantum fuzzy two-sphere Sqμ(2|2)

Abstract

In this paper, we have computed the spectrum and the [Formula: see text]-index of the super [Formula: see text]-deformed Ginsparg–Wilson Dirac operator in the different cases (fuzzy, non-fuzzy, gauged, and non-gauged) on the superquantum fuzzy two-sphere [Formula: see text]. We also presented the appropriate spin structure that this operator acts on the superquantum (Dirac) spinor bundle. Finally, it was shown that in the non-quantum limit, when [Formula: see text] tends to 1, in each case, there is a correct commutative limit for the spectrum and the [Formula: see text]-index.