Local Commutativity and Causality in Interacting PP-wave String Field Theory

TL;DR

This paper investigates how interactions in pp-wave lightcone string field theory influence local commutativity and causality, revealing that interactions do not alter commutativity conditions and highlighting differences from flat space theories.

Contribution

It extends previous work by analyzing interaction effects on causality and local commutativity in pp-wave string field theory, showing no impact of interactions on these properties.

Findings

Interaction does not affect local commutativity in pp-wave string theory

PP-wave string field theory differs from flat space in its connection properties

Discussion on the relation between local commutativity and causality in string theory

Abstract

In this paper, we extend our previous study of causality and local commutativity of string fields in the pp-wave lightcone string field theory to include interaction. Contrary to the flat space case result of Lowe, Polchinski, Susskind, Thorlacius and Uglum, we found that the pp-wave interaction does not affect the local commutativity condition. Our results show that the pp-wave lightcone string field theory is not continuously connected with the flat space one. We also discuss the relation between the condition of local commutativity and causality. While the two notions are closely related in a point particle theory, their relation is less clear in string theory. We suggest that string local commutativity may be relevant for an operational defintion of causality using strings as probes.