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

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 ${\tilde{G}}^{\alpha }$.

50 pages, Latex; v2: references added

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Cited by in corpus (13)

• Multiple Membranes in M-theory
• Knotted solutions, from electromagnetism to fluid dynamics
• Looking for a Matrix model of ABJM
• Hopf Maps, Lowest Landau Level, and Fuzzy Spheres
• Integrable domain walls in ABJM theory
• 5D Yang-Mills instantons from ABJM Monopoles
• An associative star-three-product and applications to M two/M five-brane theory
• Bifundamental Fuzzy 2-Sphere and Fuzzy Killing Spinors
• M5 brane on $R^{1,2}\times S^3$
• On Non-linear Action for Gauged M2-brane
• Dimensional reduction of the ABJM model
• Five-dimensional super Yang-Mills theory from ABJM theory
• Abelian reductions of deformed $\mathcal{N}=4$ SYM