Some Computations in Background Independent Open-String Field Theory

TL;DR

This paper computes the action for an off-shell tachyon in background independent open-string field theory, showing that on-shell, the string field action matches the world-sheet partition function when matter and ghosts are decoupled.

Contribution

It provides a concrete computation of the string field action for a specific tachyon type within background independent open-string field theory.

Findings

String field action coincides with the world-sheet partition function on-shell.

The computation demonstrates the relation between the two functions when matter and ghosts are decoupled.

The work clarifies the connection between off-shell string fields and world-sheet theories.

Abstract

Recently, background independent open-string field theory has been formally defined in the space of all two-dimensional world-sheet theories. In this paper, to make the construction more concrete, I compute the action for an off-shell tachyon field of a certain simple type. From the computation it emerges that, although the string field action does not coincide with the world-sheet (matter) partition function in general, these functions do coincide on shell. This can be demonstrated in general, as long as matter and ghosts are decoupled.