Three Lectures on String Field Theory

摘要

Presently there are several major theoretical developments whose goal is to achieve a fundamental understanding of the equations that govern the structure of string theory. In general, this basic structure is encoded in the interrelationship that exists between 2d conformal invariance and the spacetime gauge symmetries of the string theory. In an effort to formulate these explicitly, one has the approaches based on beta -functions in 2d sigma -models, S-matrix functionals, string field theory, integrable analytic geometry, loop space and others. The basic purpose of these lectures is to review some of these approaches and comment on the interrelationships that exist among them. First, we concentrate on first quantized, Polyakov string approach. The basic equations which follow from the requirement of conformal invariance are summarized. The connection with the field theoretic formulation is given based on an S-matrix generating functional method. Both the S-matrix and the field theoretic formulation still leave major open questions. These issues concern the understanding of the theory for closed strings and the orgin of general relativity. 55 refs. (ERA citation 13:031573)