Closed String Field Theory with Dynamical D-brane

TL;DR

This paper develops a closed string field theory framework with matter sources, analyzing the constraints and backreaction effects of D-branes, including recoil and boundary state modifications, within a BRST-invariant setting.

Contribution

It introduces a consistent formulation of closed string field theory with dynamical matter sources, deriving constraints and recursion relations for backreaction and D-brane recoil.

Findings

Matter current must satisfy a covariant conservation law.

Boundary states cannot serve as sources when string coupling is non-zero.

Recursion relations describe bulk backreaction and D-brane recoil.

Abstract

We consider a closed string field theory with an arbitrary matter current as a source of the closed string field. We find that the source must satisfy a constraint equation as a consequence of the BRST invariance of the theory. We see that it corresponds to the covariant conservation law for the matter current, and the equation of motion together with this constraint equation determines the classical behavior of both the closed string field and the matter. We then consider the boundary state (D-brane) as an example of a source. We see that the ordinary boundary state cannot be a source of the closed string field when the string coupling g turns on. By perturbative expansion, we derive a recursion relation which represents the bulk backreaction and the D-brane recoil. We also make a comment on the rolling tachyon boundary state.