Aspects of the gauged, twisted, SL(2|1)/SL(2|1) Wess-Zumino-Novikov-Witten model

Abstract

In this thesis we examine some of the interesting aspects of the Wess-Zumino- Novikov-Witten model when this model has been gauged and its energy tensor twisted by the addition of the derivative of one of its Cartan subalgebra valued currents. Specifically we consider the group valued model with the group taken as 5^(211) which is the Lie super group used to describe N = 2 supersymmetry. This model is advocated as being a good and natural description of the N = 2 superstring (also known as the charged spinning string, or N = 2 fermionic string) when it tensors an additional topological system of ghosts. The evidence for this assertion is presented by gauging and twisting the model and then extracting the N = 2 super Liouville action by the method of Hamiltonian reduction. The connection between the 5L (2|1)/5L (2|1) Wess-Zumino-Novikov-Witten model and field theory is made through its current algebra. As is true of many super groups there exists more than one interpretation of the Dynkin diagram for the algebra of 5L(2|1) and this results in more that one set of currents for this model. The classical and quantum currents in free field form are found in both cases, as is the highly non-linear transformation by which the two sets of currents are related. An analysis of a section of the cohomology of physical states of the model is undertaken. It is shown that the additional topological ghost system that tensors the gauged, twisted SL (2) model when it describes the N = 2 string only contributes a vacuum state to the overall cohomology, so reducing the analysis. As the 5L(2|1)/5L(2|1) Wess-Zumino-Novikov-Witten model is a topological field theory its spectrum of physical states lie in the cohomology class defined with respect to the BRST charge. The spectrum formed from the free field currents composes the so called Wakimoto module and this is calculated via the BRST formalism.