Field Theory on the q-deformed Fuzzy Sphere I
Harald Grosse, John Madore, Harold Steinacker
TL;DR
This paper explores the mathematical structure of the q-deformed fuzzy sphere, developing differential calculus, integrals, and actions for scalar and gauge fields, with applications to D-branes and WZW models.
Contribution
It introduces a compatible differential calculus and formulates field theories on the q-deformed fuzzy sphere for both real q and roots of unity.
Findings
Constructed a differential calculus compatible with star structure
Developed actions for scalar, Yang-Mills, and Chern-Simons gauge theories
Solved the zero curvature condition
Abstract
We study the q-deformed fuzzy sphere, which is related to D-branes on SU(2) WZW models, for both real q and q a root of unity. We construct for both cases a differential calculus which is compatible with the star structure, study the integral, and find a canonical frame of one-forms. We then consider actions for scalar field theory, as well as for Yang-Mills and Chern-Simons-type gauge theories. The zero curvature condition is solved.
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