IJPAM: Volume 52, No. 5 (2009)

ON ATIYAH-SINGER INDEX OF DIRAC OPERATOR ON
SIX DIMENSIONAL SPHERE WITH A $SO(6)$-GAUGE THEORY

Hünkar Kayhan$^1$, Cenap Özel$^2$
$^1$Department of Physics
Kampüsü Bolu
Abant Izzet Baysal University
Gölköy, 14280, TURKEY
e-mail: hunkar_k@ibu.edu.tr
$^2$Department of Mathematics
Kampüsü Bolu
Abant Izzet Baysal University
Gölköy, 14280, TURKEY
e-mail: cenap@ibu.edu.tr


Abstract.We consider the Dirac operator on a six dimensional sphere with gravitational and Yang-Mills gauge fields. Here we calculate the Atiyah-Singer index of Dirac operator on a six dimensional sphere with a $SO(6)$-gauge theory. Moreover, we take the vector field as to be Hedgehog-connection which gives an appropriate result for the field strength and therefore the topological charge.

Received: May 12, 2009

AMS Subject Classification: 53C07, 53Z05, 57R56, 57R20, 58J20

Key Words and Phrases: Atiyah-Singer index, Dirac operator, anomaly, topological charge, Yang-Mills fields, gravitational fields, Hedgehog connection

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 52
Issue: 5