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

TL;DR

This paper demonstrates the equivalence of two fuzzy 2-sphere constructions within the ABJM model, introduces fuzzy Killing spinors, and derives a supersymmetric D4-brane action wrapping the sphere, including fermionic sectors.

Contribution

It explicitly connects the bifundamental fuzzy sphere to the adjoint construction and derives a supersymmetric D4-brane action from ABJM fluctuations.

Findings

Fuzzy Killing spinors generate spherical harmonics.

Derived supersymmetric D4-brane action from ABJM fluctuations.

Compared twisted and untwisted D4-brane configurations.

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 $\tilde G^\alpha$.