A Review of Duality, String Vertices, Overlap Identities and the Group Theoretic Approach to String Theory

Abstract

There are three approaches to string theory; the way it was discovered which we will call the historical approach¹, the sum over world history approach² and the string field theory approach^3,4. Recently, there has been a desire to find a new formulation of string theory which incorporates the strengths of the previous approaches and is both complete and transparent, complete in the sense that it contains the whole of string theory including its perturbative and non-perturbative effects. While the perturbative effects are contained in both the string field theory and sum over world history approaches, only in the latter do the results emerge in an elegant and natural way. Alternatively, only in the former of these approaches is there the hope of computing non-perturbative effects. Since the classical string field equations in the light cone gauge and now in gauge covariant form are known, one could solve these to find classical solutions. In functional form, there is only one equation of motion, but in terms of component fields one has infinitely many equations. This makes finding solutions a formidable but not hopeless task. Given a classical solution one can, in the usual way in a field theory, find the quantum corrections. One good problem to start with is to attempt to shift the vacuum expectation values of the scalar fields to a new minimum.