Spectral triple with real structure on fuzzy sphere.

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