U(3) gauge theory on fuzzy extra dimensions

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2016-08-18

Author

Kürkcüoğlu, Seçkin

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In this article, we explore the low energy structure of a U(3) gauge theory over spaces with fuzzy sphere(s) as extra dimensions. In particular, we determine the equivariant parametrization of the gauge fields, which transform either invariantly or as vectors under the combined action of SU(2) rotations of the fuzzy spheres and those U(3) gauge transformations generated by SU(2) subset of U(3) carrying the spin 1 irreducible representation of SU(2). The cases of a single fuzzy sphere S-F(2) and a particular direct sum of concentric fuzzy spheres, S-F(2Int) F, covering the monopole bundle sectors with windings +/- 1 are treated in full and the low energy degrees of freedom for the gauge fields are obtained. Employing the parametrizations of the fields in the former case, we determine a low energy action by tracing over the fuzzy sphere and show that the emerging model is Abelian Higgs type with U(1) x U(1) gauge symmetry and possesses vortex solutions on R-2, which we discuss in some detail. Generalization of our formulation to the equivariant parametrization of gauge fields in U(n) theories is also briefly addressed.

Subject Keywords

Non-abelian vortices, Instantons

URI

https://hdl.handle.net/11511/34469

Journal

PHYSICAL REVIEW D

DOI

https://doi.org/10.1103/physrevd.94.036003

Collections

Department of Physics, Article

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Citation Formats

S. Kürkcüoğlu, “U(3) gauge theory on fuzzy extra dimensions,” PHYSICAL REVIEW D, pp. 0–0, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34469.