  Every Riemann surface with genus $g$ and $n$ punctures admits a hyperbolic
metric, if $2g-2+n>0$. Such a surface can be decomposed into pairs of pants
whose boundaries are geodesics. We construct a string field theory for closed
bosonic strings based on this pants decomposition. In order to do so, we derive
a recursion relation satisfied by the off-shell amplitudes, using the
Mirzakhani's scheme for computing integrals over the moduli space of bordered
Riemann surfaces. The recursion relation can be turned into a string field
theory via the Fokker-Planck formalism. The Fokker-Planck Hamiltonian consists
of kinetic terms and three string vertices. Unfortunately, the worldsheet BRST
symmetry is not manifest in the theory thus constructed. We will show that the
invariance can be made manifest by introducing auxiliary fields.

High Energy Physics - Theory