The Polyakov path integral over bordered surfaces. III: The BRST extended closed string off-shell amplitudes (Q1200494)

This is a continuation of the previous papers by the author [ibid. 128, No. 2, 285-318 (1990; Zbl 0692.58053); II: ibid. 139, No. 2, 353-375 (1991; Zbl 0748.58040)]. In the previous papers the path integral representation of the off-shell bosonic string amplitudes was constructed in the case of zero ghost boundary conditions. Here the above geometric method is extended in order to derive the full dependence of the off- shell amplitudes on ghost variables. Then the method is applied to construct the BRST extended off-shell amplitudes in the constant curvature ghost. In particular the overlap path integral for these amplitudes is calculated. It leads to the nonlocal sewing procedure generating all off-shell amplitudes from the cubic interaction vertex. The general scheme of the reconstruction of a covariant closed string field theory from the off-shell amplitudes is discussed within the path integral framework.