Title: Bordered surfaces, off-shell amplitudes, sewing, and string field theory
Abstract: These lectures will deal with the current status of the sewing problem. The rationale for this approach is that any nonperturbative string theory must reproduce the Polyakov path integral as a perturbation series. If our experience in ordinary field theory is a guide --- and admittedly it may not be --- the terms in such a perturbation series, like Feynman diagrams, are likely to be built up from simple ''vertices'' and ''propagators,'' which can themselves be represented as (off-shell) Polyakov amplitudes. Hence an understanding of how to put together simple components into more complicated world sheet amplitudes is likely to give us much-needed information about the structure of nonperturbative string theory. To understand sewing, we must first understand the building blocks, off-shell Polyakov amplitudes. This is the subject of my first lecture. Next, we will explore the sewing of conformal field theories at a fixed conformal structure, that is, the reconstruction of correlation functions for a fixed surface /Sigma/ from those on a pair of surfaces /Sigma//sub 1/ and /Sigma//sub 2/ obtained by cutting /Sigma/ along a closed curve. We will then look at the problem of sewing amplitudes, integrals of correlation functions over moduli space. This will necessitate anmore » understanding of how to build the moduli space of a complicated surface from simpler moduli spaces. Finally, we will briefly examine vertices and string field theories. 48 refs., 10 figs.« less