Dynamics of WessZuminoWitten and ChernSimons Theories
Abstract
This thesis is devoted to the study of three problems on the WessZuminoWitten (WZW) and ChernSimons (CS) supergravity theories in the Hamiltonian framework: 1) The twodimensional super WZW model coupled to supergravity is constructed. The canonical representation of KacMoody algebra is extended to the super KacMoody and Virasoro algebras. Then, the canonical action is constructed, invariant under local supersymmetry transformations. The metric tensor and RaritaSchwinger fields emerge as Lagrange multipliers of the components of the super energymomentum tensor. 2) In higher dimensions, CS theories are irregular systems, that is, they have constraints which are functionally dependent in some sectors of phase space. In these cases, the standard Dirac procedure must be redefined, as it is shown in the simplified case of finite number of degrees of freedom. Irregular systems fall into two classes depending on their behavior in the vicinity of the constraint surface. In one case, it is possible to regularize the system without ambiguities, while in the other, regularization is not always possible and the Hamiltonian and Lagrangian descriptions may be dynamically inequivalent. Irregularities have important consequences in the linearized approximation of nonlinear theories. 3) The dynamics of CS supergravity theory in D=5, based on the supersymmetric extension of the AdS algebra, su(2,24), is analyzed. A class of backgrounds is found, providing a regular and generic effective theory. Some of these backgrounds are shown to be BPS states. The charges for the simplest choice of asymptotic conditions are obtained, and they satisfy a supersymmetric extension of the classical WZW(4) algebra, associated to su(2,24).
 Publication:

arXiv eprints
 Pub Date:
 January 2004
 arXiv:
 arXiv:hepth/0401185
 Bibcode:
 2004hep.th....1185M
 Keywords:

 High Energy Physics  Theory
 EPrint:
 Ph.D. Thesis, January 2004, 125 pages, no figures