Conformal Field Theory and the Holgoraphic Principle

Abstract: This thesis is based on five research papers with string theory as the least common denominator. The text is divided in two parts. The first part is an introduction to the constructions used in the papers; string theory, conformal field theory, topological field theory and three-dimensional gravity. The second part is a review of a concept believed to be important in any theory of quantum gravity, the so called holographic principle.



A relation between three-dimensional topological field theory and two-dimensional conformal field theory is re-established in a classical formulation. This result is then used to investigate holography in a toy model, gravity in three dimensions. A construction is proposed which yields the Bekenstein-Hawking entropy of a three-dimensional black hole. The same mechanism is shown not to be responsible for the entropy of Kerr-de Sitter spacetime.

Similar methods yields a relation between topological field theories in five and seven dimensions and chiral conformal field theories in four and six dimensions.



There presumably exists a class of conformal field theories with novel properties, so called logarthmic conformal field theories. By starting from a conventional theory, a systematic way to deform this to a logarithmic theory is developed.