D1-brane in Constant R-R 3-form Flux and Nambu Dynamics in String Theory

Abstract

We consider D1-string in a constant R-R 3-form flux background and analyze its low energy limit. The leading order low energy theory has reparametrization symmetry and is a generalization of an earlier work by Takhtajan. We show that the dynamical evolution of the theory takes a generalized Hamiltonian form in terms of a Nambu bracket. This description is formulated in terms of reparametrization invariant quantities and requires no fixing of the reparametrization symmetry. We also show that a Nambu- Poisson (p + 2)-bracket arises naturally in the reparametrization invariant description of the low energy theory of a p-brane in a constant (p + 2)-form flux background. For example, our results apply for a fundamental string in a constant NS-NS 3-form flux H3 and an M2-brane in a constant 4-form flux F4.

30 pages, latex, references added

References in corpus (9)

• On Foundation of the Generalized Nambu Mechanics
• On the Quantization of Nambu Brackets
• Deformation Quantization and Nambu Mechanics
• A Noncommutative M-Theory Five-brane
• Open membranes in a constant C-field background and noncommutative boundary strings
• Deformation Quantization of Superintegrable Systems and Nambu Mechanics
• Volume Preserving Diffeomorphism and Noncommutative Branes
• Nambu Bracket for M Theory
• Three-algebra for supermembrane and two-algebra for superstring

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