Super Yang-Mills Theory on Noncommutative Torus from Open Strings Interactions

TL;DR

This paper demonstrates that scattering amplitudes of open strings on a D2-brane in a B-field background match the predictions of noncommutative gauge theory, specifically involving the Moyal bracket, up to order α'^2.

Contribution

It establishes a precise correspondence between open string scattering amplitudes and noncommutative gauge theory on a D-brane with a B-field, including higher-order corrections.

Findings

Scattering amplitudes match noncommutative gauge theory predictions up to α'^2 order.

The noncommutative structure is characterized by the Moyal bracket.

Provides a string-theoretic derivation of noncommutative gauge interactions.

Abstract

Considering the scattering of massless open strings attached to a D2-brane living in the $B$ field background, we show that corresponding scattering upto the order of $\a'^2$ is exactly given by the gauge theory on noncommutative background, which is characterized by the Moyal bracket.