Cubic String Field Theory in pp-wave Background and Background Independent Moyal Structure

TL;DR

This paper explores the structure of open string field theory in a pp-wave background, revealing a universal Moyal product structure and identifying operators related to D-branes, advancing understanding of string interactions in this setting.

Contribution

It demonstrates that Witten's *-product in the pp-wave background can be represented as a universal Moyal product, independent of the background, and connects algebraic operators to D-branes.

Findings

Witten *-product is equivalent to infinite copies of Moyal product with θ=2

The Moyal structure is universal across backgrounds in the string bit basis

Identification of projective operators as D-branes

Abstract

We study Witten open string field theory in the pp-wave background in the tensionless limit, and construct the N-string vertex in the basis which diagonalizes the string perturbative spectrum. We found that the Witten *-product can be viewed as infinite copies of the Moyal product with the same noncommutativity parameter $\theta=2$. Moreover, we show that this Moyal structure is universal in the sense that, written in the string bit basis, Witten's *-product for any background can always be given in terms of the above-mentioned Moyal structure. We identify some projective operators in this algebra that we argue to correspond to D-branes of the theory.