Abstract
We present an explicit matrix algebra regularization of the algebra of volume-preserving diffeomorphisms of the n-torus. That is, we approximate the corresponding classical Nambu brackets using mathfrak{sl}left({N}^{leftlceil frac{n}{2}rightrceil },mathrm{mathbb{C}}right) -matrices equipped with the finite bracket given by the completely anti-symmetrized matrix product, such that the classical brackets are retrieved in the N → ∞ limit. We then apply this approximation to the super 4-brane in 9 dimensions and give a regularized action in analogy with the matrix regularization of the supermembrane. This action exhibits a reduced gauge symmetry that we discuss from the viewpoint of L∞-algebras in a slight generalization to the construction of Lie 2-algebras from Bagger-Lambert 3-algebras.
Highlights
We present an explicit matrix algebra regularization of the algebra of volumepreserving diffeomorphisms of the n-torus
We approximate the corresponding n classical Nambu brackets using sl(N 2, C)-matrices equipped with the finite bracket given by the completely anti-symmetrized matrix product, such that the classical brackets are retrieved in the N → ∞ limit
De Wit et al [6] proposed a finite-N regularization, in which the above action in the light-cone gauge is regularized by an appropriate sl(N, C)-matrix gauge theory. This was based on approximating the algebra of area-preserving diffeomorphisms which correspond to the residual symmetries of the supermembrane after imposing the light-cone gauge
Summary
We shall first review the relevant facts concerning the gauge-fixing and regularization of the Green-Schwarz supermembrane action, which underlies the BFSS matrix model. More details and further background material can be found in the reviews [22, 23]. We discuss how the gauge-fixing generalizes to higher dimensional super p-brane actions and pose the problem of their matrix regularization
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
