Topological defects in conformal field theory and string theory

The current view of theoretical physics on the workings of Nature is based on two main pillars: general relativity, which describes physics at large scales, like the solar system and beyond, and quantum field theory, which describes the microscopic constituents of matter, like electrons and quarks. Both theories are in perfect agreement with experiment, but to date no mathematically consistent unified formulation, which includes both these theories as appropriate limits, has been found. There are, of course, candidates, and one such candidate is called string theory. While in quantum field theory one thinks of the fundamental particles, e.g. the electrons, as point-like without an extend in any direction of space, in string theory the fundamental particle is a tiny loop. String theory is mathematically highly involved, and it has been impossible so far to make unambiguous contact between experiments and predictions of string theory. The aim of the project is to understand better the mathematical foundations of string theory, in particular its symmetries. This is to be achieved with the help of so-called two-dimensional conformal quantum field theory. The latter describes how the strings, i.e. the tiny loops mentioned above, move in space. In this project the conformal field theory will be investigated in great detail. This will, for example, allow one to understand precisely how a loop of string can get deformed into a figure eight and then split into two loops, or how such a loop can break open at one point and then move in space as a piece of string with two loose ends.This project will provide one more piece in the big puzzle whose ultimate goal is to decide, in the positive or in the negative, if string theory can provide the desired unified description of all the forces we see in Nature.