Non-commutative superspace from string theory

TL;DR

This paper explores how background fields in string theory induce non-commutative structures in ten-dimensional superspace, extending known four-dimensional results to a more general setting with implications for supersymmetric geometry.

Contribution

It demonstrates that RR fields and gravitino backgrounds lead to non-commutative relations in ten-dimensional superspace, generalizing previous four-dimensional findings.

Findings

RR field strengths induce non-zero {θ,θ} anti-commutators

Gravitino backgrounds produce non-zero [x,θ] commutators

Extension of non-commutative superspace from 4D to 10D

Abstract

Turning on background fields in string theory sometimes has an alternative interpretation as a deformation of the target space geometry. A particularly well-known case is the NS-NS two form B, which gives rise to space-time non-commutativity. In this note we point out that this phenomenon extends to ten-dimensional superspace when employing a covariant quantization of the superstring, generalizing an observation by Ooguri and Vafa in four dimensions. In particular, we will find that RR field strengths give rise to a non-zero $\{\theta,\theta\}$ anti-commutator, just as in four dimensions, whereas the gravitino yields a non-zero value for $[x,\theta]$.