Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 058, 28 pages      arXiv:1003.5590
Contribution to the Special Issue “Noncommutative Spaces and Fields”

Bifundamental Fuzzy 2-Sphere and Fuzzy Killing Spinors

Horatiu Nastase a and Constantinos Papageorgakis b
a) Instituto de Física Teórica, UNESP-Universidade Estadual Paulista, R. Dr. Bento T. Ferraz 271, Bl. II, Sao Paulo 01140-070, SP, Brazil
b) Department of Mathematics, King's College London, The Strand, London WC2R 2LS, UK

Received March 26, 2010, in final form July 09, 2010; Published online July 20, 2010

We review our construction of a bifundamental version of the fuzzy 2-sphere and its relation to fuzzy Killing spinors, first obtained in the context of the ABJM membrane model. This is shown to be completely equivalent to the usual (adjoint) fuzzy sphere. We discuss the mathematical details of the bifundamental fuzzy sphere and its field theory expansion in a model-independent way. We also examine how this new formulation affects the twisting of the fields, when comparing the field theory on the fuzzy sphere background with the compactification of the 'deconstructed' (higher dimensional) field theory.

Key words: noncommutative geometry; fuzzy sphere; field theory.

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