An extension of the Polyakov path-integral formulation to compute off-shell amplitudes for open bosonic strings is derived. Boundary conditions require evaluating the path integral on open surfaces with corners on the boundaries. The contribution to the topological term in the action from the corners is exactly that required for unitarity. The presence of corners introduces a Weyl anomaly in the Polyakov measure. This requires a gauge-fixing procedure for the off-shell amplitudes. Consistent factorization of amplitudes with one or two off-shell strings and any number of on-shell tachyons is established.

• Received 14 September 1987

DOI:https://doi.org/10.1103/PhysRevD.37.981