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arXiv · 0908.3263

Fuzzy Killing Spinors and Supersymmetric D4 action on the Fuzzy 2-sphere from the ABJM Model

Horatiu Nastase·Constantinos Papageorgakis
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Abstract

Our recent construction arXiv:0903.3966 for the fuzzy 2-sphere in terms of bifundamentals, discovered in the context of the ABJM model, is shown to be explicitly equivalent to the usual (adjoint) fuzzy sphere construction. The matrices $\tilde G^\alpha$ that define it play the role of fuzzy Killing spinors on the 2-sphere, out of which all spherical harmonics are constructed. Starting from the quadratic fluctuation action around these solutions in the mass-deformed ABJM theory, we recover a supersymmetric D4-brane action wrapping a 2-sphere, including fermions. We obtain both the usual D4 action with an unusual x-dependence on the sphere, as well as a twisted version in terms of the usual x-dependence, and contrast our result with the Maldacena-Nunez case of a D5 wrapping an S^2. The twisted and unwisted fields are related by the same matrix $\tilde G^\alpha$.

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Horatiu Nastase, Constantinos Papageorgakis. 2009-08-22. Fuzzy Killing Spinors and Supersymmetric D4 action on the Fuzzy 2-sphere from the ABJM Model. https://doi.org/10.1088/1126-6708/2009/12/049

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