Space/Time Noncommutativity in String Theories without Background Electric Field

TL;DR

This paper explores how space/time non-commutativity arises in open string theories with specific background metrics, even without electric fields, and examines the effects on string spectra and thermodynamics.

Contribution

It demonstrates that a Moyal phase can appear without electric fields in certain string backgrounds and provides a proper definition of vertex operators in this context.

Findings

A Moyal phase arises even without electric fields in specific backgrounds.

The theory is dual to non-commutative open string (NCOS) theory.

The Hagedorn temperature depends non-extensively on background parameters.

Abstract

The appearance of space/time non-commutativity in theories of open strings with a constant non-diagonal background metric is considered. We show that, even if the space-time coordinates commute, when there is a metric with a time-space component, no electric field and the boundary condition along the spatial direction is Dirichlet, a Moyal phase still arises in products of vertex operators. The theory is in fact dual to the non-commutatitive open string (NCOS) theory. The correct definition of the vertex operators for this theory is provided. We study the system also in the presence of a $B$ field. We consider the case in which the Dirichlet spatial direction is compactified and analyze the effect of these background on the closed string spectrum. We then heat up the system. We find that the Hagedorn temperature depends in a non-extensive way on the parameters of the background and it is the same for the closed and the open string sectors.