Quantum geometrodynamics of the open topological membrane and string moduli space

We show that by coupling a three-dimensional Chern-Simons theory to (2+1)-dimensional gravity through an arbitrarily small ${\mathit{F}}^2$ term, one can obtain integrals of conformal-field-theory amplitudes over moduli space. The conformal anomaly appears as an induced gravitational Chern-Simons term. String-theory amplitudes can thus be obtained from three dimensions.