Related papers: Matrix Quantization of Classical Nambu Brackets and Super $p$-Branes

Matrix Quantization of Classical Nambu Brackets and Super $p$-Branes

URL: http://arxiv.org/abs/2103.06666v3
Date: Thu, 6 Jan 2022 18:11:05 GMT
Title: Matrix Quantization of Classical Nambu Brackets and Super $p$-Branes
Authors: Meer Ashwinkumar, Lennart Schmidt, Meng-Chwan Tan
Abstract summary: We present an explicit matrix algebra quantization of the algebra of volume-preserving diffeomorphisms of the $n$-torus. We approximate the corresponding classical Nambu brackets using $mathfraksl(Nlceilfracn2rceil,mathbbC)$-matrices equipped with the finite bracket given by the completely anti-symmetrized matrix product.
Score: 0.5156484100374059
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We present an explicit matrix algebra quantization of the algebra of volume-preserving diffeomorphisms of the $n$-torus. That is, we approximate the corresponding classical Nambu brackets using $\mathfrak{sl}(N^{\lceil\frac{n}{2}\rceil},\mathbb{C})$-matrices equipped with the finite bracket given by the completely anti-symmetrized matrix product, such that the classical brackets are retrieved in the $N\rightarrow \infty$ limit. We then apply this approximation to the super $4$-brane in $9$ dimensions and give a regularized action in analogy with the matrix quantization of the supermembrane. This action exhibits a reduced gauge symmetry that we discuss from the viewpoint of $L_\infty$-algebras in a slight generalization to the construction of Lie $2$-algebras from Bagger--Lambert $3$-algebras.

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