Free (2,0) Theory on a Circle Fibration

Abstract

Using the geometry of a circle fibration the free (2,0) theory, a six dimensional superconformal field theory, is reduced to a five dimensional abelian Yang-Mills theory. The six dimensional theory is conjectured to exist as an interacting theory but as of this time no consistent formulation of the theory is known. In this thesis a simpler non-interacting, classical version of the theory is considered on a six dimensional space-time which is a circle fibration over a curved five dimensional manifold. It is found that the reduced theory in five dimensions has a supersymmetric Lagrangian description. This thesis starts by giving an introduction to the mathematical formalism used in field theory on curved spacetime and continues to describe the free (2,0) theory in six dimensions. The reduction on the circle fibration is then presented together with the resulting five dimensional theory.