Closed String Field Theory in 25.99 Dimensions

TL;DR

This paper refines closed string field theory in non-critical backgrounds, constructing the BV action and extending background independence to first order off the conformal locus, with applications to non-critical string theories.

Contribution

It develops a formalism for closed string field theory in non-critical dimensions, including BV action construction and background independence extension.

Findings

Constructed mixed moduli spaces for the classical BV action.

Proved existence of these moduli spaces.

Extended background independence to first order off the conformal locus.

Abstract

We return to and refine Zwiebach's formulation of closed string field theory (CSFT) built around non-critical backgrounds [1,2], restricting our attention to genus zero. The structure involves a special string state $F$ that encodes the failure of worldsheet BRST invariance, and a metric-dependent descent operator $\mathcal{B}$ adapted to the Weyl frame. We construct the mixed moduli spaces needed for the classical BV action, prove their existence, and extend the Sen-Zwiebach background independence argument to first order off of the conformal locus. We apply the formalism to the mildest deviation away from criticality - worldsheet CFTs with nonzero central charge: we consider both D=26-$\epsilon$ dimensional flat space and linear dilaton profiles in bosonic string theory, focusing for simplicity on building solutions that depend on only one of the D dimensions.