Gauge Invariant Closed String Field Theory and the Virasoro-Shapiro Amplitude

Using a gauge invariant closed string field theory recently proposed by us, we show that the amplitude for 4tachyon scattering in our theory is given by the ViiasoreShapiro amplitude. It is widely believed (or hoped!) that string field theory will give us a han-dle on possible non-perturbative ground states of the string, analogous to the Schwarzschildsolution in general relativity. For this reason, among others, it would be extremely useful to construct gauge invariant, interacting string field theories. Witten [l] has proposed such a theory for the open string. Hi construction involves the definition of a non-commutative differential geometry, where string fields are treated as one-forms (as advocated by Banks and Peskin 121) and the BRST charge Q acts ss the exterior derivative (in the critical dimension only!). An integral and wedge product are then defined for these forms by considering string path integrals over appropriately chosen 2-D surfaces. From this formalism a non-linear gauge invariance can be formulated, whose linear piece had been considere