Spectral triple with real structure on fuzzy sphere

In this paper, we have illustrated the construction of a real structure on fuzzy sphere S*2 in its spin-1/2 representation. Considering SU(2) covariant Dirac and chirality operator given by U. C. Watamura [Commun. Math. Phys. 183, 365–382 (1997) Commun. 212, 395–413 (2000)], shown that is consistent with other spectral data for KO dimension-4 fulfilling zero order condition, where find it necessary to enlarge symmetry group from SO(3) full orthogonal O(3). However, first condition violated, thus paving way construct toy model an gauge theory capture some features physics beyond standard following Chamseddine et al. (J. High Energy 2013, 132).