Closed String Field Theory in 25.99 Dimensions

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.