Matrix regularization of classical Nambu brackets and super p-branes
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 sl N n 2 ℂ $$ \mathfrak{sl}\left({N}^{\left\lceil \frac{n}{2}\right\rceil },\mathrm{\mathbb{C}}\r...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2021-07-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP07(2021)172 |
| Summary: | Abstract We present an explicit matrix algebra regularization of the algebra of volume-preserving diffeomorphisms of the n-torus. That is, we approximate the corresponding classical Nambu brackets using sl N n 2 ℂ $$ \mathfrak{sl}\left({N}^{\left\lceil \frac{n}{2}\right\rceil },\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. |
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| ISSN: | 1029-8479 |