EFFECTIVE TACHYONIC POTENTIAL IN CLOSED STRING FIELD-THEORY

We calculate the effective tachyonic potential in closed string field theory up to the quartic term in the tree approximation. This involves an elementary four-tachyon vertex and a sum over the infinite number of Feynman graphs with an intermediate massive state. We show that both the elementary term and the sum can be evaluated as integrals of some measure over different regions in the moduli space of four-punctured spheres. We show that both elementary and effective couplings give negative contributions to the quartic term in the tachyon potential. Numerical calculations show that the fourth-order term is big enough to destroy a local minimum which exists in the third-order approximation.