Quantum Dynamics on the Worldvolume from Classical $\mathrm{su}(n)$ Cohomology

José M. Isidro ; Pedro Fernández de Córdoba

Symmetry, integrability and geometry: methods and applications, Tome 4 (2008)

Résumé

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 $\mathrm{su}(n)$, 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 $\mathrm{su}(n)$.

Détail

Keywords: branes; Nambu brackets; Lie-algebra cohomology.

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