Matrix Strings in Weakly Curved Background Fields

TL;DR

This paper derives a Matrix string theory action in weak, curved background fields, incorporating R-R fluxes and dualities, and explores noncommutative effects and background curvature corrections for multiple strings.

Contribution

It provides a new derivation of the Matrix string action in weak backgrounds using dualities and discusses non-linear curvature corrections and noncommutative string configurations.

Findings

Derived Matrix string action in weak, curved backgrounds.

Established explicit duality relations and S-duality implementation.

Illustrated noncommutative polarization effects of multiple strings in R-R flux.

Abstract

We investigate further the recent proposal for the form of the Matrix theory action in weak background fields. We perform DVV reduction to the multiple D0-brane action in order to find the Matrix string theory action for multiple fundamental strings in curved but weak NS-NS and R-R backgrounds. This matrix sigma model gives a definite prescription on how to deal with R-R fields with an explicit spacetime dependence in Type II string theory. We do this both via the 9-11 flip and the chain of T and S dualities, and further check on their equivalence explicitly. In order to do so, we also discuss the implementation of S-duality in the operators of the 2-dimensional world-volume supersymmetric gauge theory describing the Type IIB D-string. We compare the result to the known Green-Schwarz sigma model action (for one string), and use this comparison in order to discuss about possible, non-linear background curvature corrections to the Matrix string action (involving many strings), and therefore to the Matrix theory action. We illustrate the nonabelian character of our action with an example involving multiple fundamental strings in a non-trivial R-R flux, where the strings are polarized into a noncommutative configuration. This corresponds to a dielectric type of effect on fundamental strings.