TWO-LOOP BETA FUNCTION IN THE OPEN STRING SIGMA MODEL AND EQUIVALENCE WITH STRING EFFECTIVE EQUATIONS OF MOTION

We consider the sigma-model on the disc corresponding to the open bose string in external abelian vector field and compute the order ∂3F3-terms in its two-loop β-function. The vanishing of the two-loop β-function (modulo diffeomorphism and gauge terms) is shown to be equivalent (to the given order) to the equation of motion for the string theory effective action reconstructed from the string scattering amplitudes.