Conformal Perturbation Theory and Tachyon-Dilaton Eschatology via String Fields

We analyze deformations of two-dimensional conformal field theory (CFT) from the perspective of classical bosonic closed string field theory (SFT). The latter can be viewed as a version of Wilsonian renormalization group (RG) improved conformal perturbation theory, where the renormalization scheme is defined through the choice of string vertices in the construction of SFT. Furthermore, the CFT data at the RG fixed point can be recovered from the spectrum and amplitudes of string field fluctuations. As applications, we construct the Horowitz-Polchinski "string star" solution in SFT, and a solution of tachyon-dilaton condensation that deforms the noncompact boson to minimal models by creating a pair of "Runkel-Watts walls".