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Monopoles, Dirac operator, and index theory for fuzzy SU(3) / (U(1) x U(1))

Acharyya, Nirmalendu and Diez, Veronica Errasti (2014) Monopoles, Dirac operator, and index theory for fuzzy SU(3) / (U(1) x U(1)). In: PHYSICAL REVIEW D, 90 (12).

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Official URL: http://dx.doi.org/ 10.1103/PhysRevD.90.125034


The intersection of the ten-dimensional fuzzy conifold Y-F(10) with S-F(5) x S-F(5) is the compact eight-dimensional fuzzy space X-F(8). We show that X-F(8) is (the analogue of) a principal U(1) x U(1) bundle over fuzzy SU(3) / U(1) x U(1)) ( M-F(6)). We construct M-F(6) using the Gell-Mann matrices by adapting Schwinger's construction. The space M-F(6) 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 M-F(6) 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.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the AMER PHYSICAL SOC, ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 06 Feb 2015 14:48
Last Modified: 06 Feb 2015 14:48
URI: http://eprints.iisc.ac.in/id/eprint/50777

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