TFD Extension of Open String Field Theory

TL;DR

This paper applies Thermo Field Dynamics to open string field theory, extending the state space to include statistical and entanglement effects, revealing new degrees of freedom and maintaining consistency with conventional interactions.

Contribution

It introduces a TFD-based extension of OSFT, incorporating statistical and entanglement features, and demonstrates how to modify the interaction vertices accordingly.

Findings

New fields emerge due to quantum entanglement.

The extended theory includes degrees of freedom resembling closed strings.

Tree-level interactions match conventional OSFT results.

Abstract

We study the application of the rules of Thermo Field Dynamics (TFD) to the covariant formulation of Open String Field Theory (OSFT). We extend the states space and fields according to the duplication rules of TFD and construct the corresponding classical action. The result is interpreted as a theory whose fields would encode the statistical information of open strings. The physical spectrum of the free theory is studied through the cohomology of the extended BRST charge, and, as a result, we get new fields in the spectrum emerging by virtue of the quantum entanglement and, noticeably, it presents degrees of freedom that could be identified as those of closed strings. We also show, however, that their appearing in the action is directly related to the choice of the inner product in the extended algebra, so that different sectors of fields could be eliminated from the theory by choosing that product conveniently. Finally, we study the extension of the three-vertex interaction and provide a simple prescription for it whose results at tree-level agree with those of the conventional theory.