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

TL;DR

This paper explores the low energy dynamics of D1-strings in a constant R-R 3-form flux, revealing a Nambu bracket structure that generalizes Hamiltonian mechanics and applies to various p-branes in flux backgrounds.

Contribution

It demonstrates that the low energy theory of D1-strings in flux backgrounds can be described using a Nambu bracket, extending previous work and providing a reparametrization invariant formulation.

Findings

Reparametrization symmetry is preserved in the low energy limit.

A Nambu-Poisson (p+2)-bracket naturally arises in the theory.

The framework applies to fundamental strings and M2-branes in flux backgrounds.

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.