par Acharyya, Nirmalendu ;Errasti Díez, Verónica
Référence Physical Review D - Particles, Fields, Gravitation and Cosmology, 90, 12, 125034
Publication Publié, 2014-12-30
Article révisé par les pairs
Résumé : The intersection of the ten-dimensional fuzzy conifold YF10 with SF5×SF5 is the compact eight-dimensional fuzzy space XF8. We show that XF8 is (the analogue of) a principal U(1)×U(1) bundle over fuzzy SU(3)/(U(1)×U(1))(≡MF6). We construct MF6 using the Gell-Mann matrices by adapting Schwinger’s construction. The space MF6 is of relevance in higher dimensional quantum Hall effect and matrix models of D-branes. Further we show that the sections of the monopole bundle can be expressed in the basis of SU(3) eigenvectors. We construct the Dirac operator on MF6 from the Ginsparg-Wilson algebra on this space. Finally, we show that the index of the Dirac operator correctly reproduces the known results in the continuum.