Conformal Field Theory Deformations and Supersymmetric D-brane Actions
Over the past few years a dramatic progress in understanding non-perturbative phenomena in string theory has occurred. This is commonly referred to as the second string revolution. This thesis, consisting of an introduction and five appended research papers (I-V), deals with pre-revolutionary as well as post-revolutionary aspects of string theory.
In the introduction we give a brief overview of string theory relevant for the research papers.
In chapter 2 we make a rather thorough presentation of two-dimensional conformal field theories defined both on the sphere and on higher genus surfaces. This is motivated by research papers I and II where we deform the conformal structure of closed bosonic string theory, using primary fields of conformal weight (1,1) also known as marginal operators. In paper I a canonical surface integral formulation is developed and in particular a unique regularization is introduced. This analytic regularization is then used in paper II to study connections on the space of conformal field theories. The connections are shown to be flat and to generate well-defined finite parallel transports.
In chapter 3 we present perturbative string theory leading up to the five consistent superstring theories. In chapter 4 we make a very brief description of closed bosonic string theory, trying to further motivate the work of papers I and II.
Duality is the subject of chapter 5. Here we present the web of dualities between the different string theories, trying to emphasis the important role played by p-branes and D-branes. Chapter 6, the last chapter of the introduction, further discusses the role played by p-branes and D-branes. The low energy effective actions of p-branes and D-branes are presented. This is heavily motivated by papers III-V, which address and solve the problem of formulating low energy effective supersymmetric D-brane actions propagating in a curved type II supergravity background.