Quantum Dynamics on the Worldvolume from Classical su(n) Cohomology

Abstract

A key symmetry of classical $p$-branes is invariance under worldvolume diffeomorphisms. Under the assumption that the worldvolume, at fixed values of the time, is a compact, quantisable Kähler manifold, we prove that the Lie algebra of volume-preserving diffeomorphisms of the worldvolume can be approximated by $su(n)$, for $n\to \infty$. We also prove, under the same assumptions regarding the worldvolume at fixed time, that classical Nambu brackets on the worldvolume are quantised by the multibrackets corresponding to cocycles in the cohomology of the Lie algebra $su(n)$.

This is a contribution to the Special Issue on Deformation Quantization, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

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Cited by in corpus (1)

• Relaxed Three-Algebras: Their Matrix Representations and Implications for Multi M2-brane Theory