The cosmological constant of modular closed string field theory. I

We formulate closed string field theory as a quantum theory of modular geometry. We determine the full interacting quantum hamiltonian to all loop orders in perturbation theory. The free action has a new highly non-linear symmetry acting on the string field, and the kinetic operator. Perturbatively we demonstrate that the new theory gives the correct expression for the cosmological constant that is ultraviolet finite to one-loop order.