NON-ABELIAN POISSON MANIFOLDS FROM D-BRANES

DOI10.1142/S0217732304015671zbMath1158.81350arXivhep-th/0407226MaRDI QIDQ4674066

José M. Isidro

Publication date: 9 May 2005

Published in: Modern Physics Letters A (Search for Journal in Brave)

Abstract: Superimposed D-branes have matrix-valued functions as their transverse coordinates, since the latter take values in the Lie algebra of the gauge group inside the stack of coincident branes. This leads to considering a classical dynamics where the multiplication law for coordinates and/or momenta, being given by matrix multiplication, is nonabelian. Quantisation further introduces noncommutativity as a deformation in powers of Planck's constant. Given an arbitrary simple Lie algebra and an arbitrary Poisson manifold, both finite-dimensional, we define a corresponding C*-algebra that can be regarded as a nonabelian Poisson manifold. The latter provides a natural framework for a matrix-valued classical dynamics.

Full work available at URL: https://arxiv.org/abs/hep-th/0407226

zbMATH Keywords

\(D\)-branesPoisson brackets

Mathematics Subject Classification ID

String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Poisson manifolds; Poisson groupoids and algebroids (53D17)

Cites Work

• M-theory and Seiberg-Witten curves: orthogonal and symplectic groups
• Bound states of strings and \(p\)-branes

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