Symmetries and degrees of freedom in 2-dimensional dual models

The 2-dimensional version of the Schwarz and Sen duality model (Tseytlin model) is analyzed at the classical and quantum levels. The solutions are obtained after removing the gauge dependent sector using the Dirac method. The Poincar\`e invariance is verified at both levels. An extension with global supersymmetry is also proposed.Comment: 3 pages, revtex, minor correction

Loop Quantization of the Supersymmetric Two-Dimensional BF Model

In this paper we consider the quantization of the 2d BF model coupled to topological matter. Guided by the rigid supersymmetry this system can be viewed as a super-BF model, where the field content is expressed in terms of superfields. A canonical analysis is done and the constraints are then implemented at the quantum level in order to construct the Hilbert space of the theory under the perspective of Loop Quantum Gravity methods.Comment: 17 pages, Late

Observables in Topological Yang-Mills Theories

Using topological Yang-Mills theory as example, we discuss the definition and determination of observables in topological field theories (of Witten-type) within the superspace formulation proposed by Horne. This approach to the equivariant cohomology leads to a set of bi-descent equations involving the BRST and supersymmetry operators as well as the exterior derivative. This allows us to determine superspace expressions for all observables, and thereby to recover the Donaldson-Witten polynomials when choosing a Wess-Zumino-type gauge.Comment: 39 pages, Late

Complete loop quantization of a dimension 1+2 Lorentzian gravity theory

De Sitter Chern-Simons gravity in D = 1 + 2 spacetime is known to possess an extension with a Barbero-Immirzi like parameter. We find a partial gauge fixing which leaves a compact residual gauge group, namely SU(2). The compacticity of the residual gauge group opens the way to the usual LQG quantization techniques. We recall the exemple of the LQG quantization of SU(2) CS theory with cylindrical space topology, which thus provides a complete LQG of a Lorentzian gravity model in 3-dimensional space-time.Comment: Loops11 - Madrid - 2011 (4 pages, Latex

Symmetries and observables in topological gravity

After a brief review of topological gravity, we present a superspace approach to this theory. This formulation allows us to recover in a natural manner various known results and to gain some insight into the precise relationship between different approaches to topological gravity. Though the main focus of our work is on the vielbein formalism, we also discuss the metric approach and its relationship with the former formalism.Comment: 34 pages; a few explanations added in subsection 2.2.1, published version of pape