Clisthenis P. Constantinidis

Regular bouncing cosmological solutions in effective actions in four dimensions

We study cosmological scenarios resulting from effective actions in four dimensions which are, under some assumptions, connected with multidimensional, supergravity and string theories. These effective actions are labeled by the parameters

Quantization of the Jackiw-Teitelboim model

ensuremath{omega},

Superspace gauge fixing of topological Yang-Mills theories

the dilaton coupling constant, and n which establishes the coupling between the dilaton and a scalar field originating from the gauge field existing in the original theories. There is a large class of bouncing as well as Friedmann-like solutions. We investigate under which conditions bouncing regular solutions can be obtained. In the case of the string effective action, regularity is obtained through the inclusion of contributions from the Ramond-Ramond sector of superstring.

Quantization of Lorentzian 3D gravity by partial gauge fixing

We study the phase space structure of the Jackiw-Teitelboim model in its connection variables formulation where the gauge group of the field theory is given by local SL(2,R)[or SU(2) for the Euclidean model], i.e. the de Sitter group in two dimensions. In order to make the connection with two-dimensional gravity explicit, a partial gauge fixing of the de Sitter symmetry can be introduced that reduces it to space-time diffeomorphisms. This can be done in different ways. Having no local physical degrees of freedom, the reduced phase space of the model is finite dimensional. The simplicity of this gauge field theory allows for studying different avenues for quantization, which may use various (partial) gauge fixings. We show that reduction and quantization are noncommuting operations: the representation of basic variables as operators in a Hilbert space depends on the order chosen for the latter. Moreover, a representation that is natural in one case may not even be available in the other leading to inequivalent quantum theories.

Topological Yang-Mills Theories and their Observables: A Superspace Approach

Abstract.We revisit the construction of topological Yang-Mills theories of the Witten type with arbitrary space-time dimension and number of “shift supersymmetry” generators, using a superspace formalism. The super-BF structure of these theories is exploited in order to determine their actions uniquely, up to the ambiguities due to the fixing of the Yang-Mills and BF gauge invariance. UV finiteness to all orders of perturbation theory is proved in a gauge of the Landau type.

Solution to the zero-Hamiltonian problem in 2D gravity

D = 2 + 1 gravity with a cosmological constant Λ has been shown by Bonzom and Livine to present a Barbero–Immirzi-like ambiguity depending on a parameter γ. We make use of this fact to show that, for Λ >0, the Lorentzian theory can be partially gauge fixed and reduced to an SU(2) Chern–Simons theory. We then review the already known quantization of the latter in the framework of loop quantization for the case of space being topologically a cylinder. We finally construct, in the same setting, a quantum observable which, although non-trivial at the quantum level, corresponds to a null classical quantity.

Falsifying tree level string motivated bouncing cosmologies

Wittens observables of topological Yang-Mills theory, defined as classes of an equivariant cohomology, are reobtained as the BRST cohomology classes of a superspace version of the theory.

Observables in topological Yang-Mills theorieswith extended shift supersymmetry

The zero-Hamiltonian problem, present in reparametrization invariant systems, is solved for the 2D induced gravity model. Working with methods developed by Henneaux, Teitelboim, and Vergara we find, systematically, reduced phase-space physics, generated by an effective Hamiltonian obtained after complete gauge fixing.

Symmetries and Observables in Topological Gravity

The string effective action at tree level contains, in its bosonic sector, the Einstein-Hilbert term, the dilaton, and the axion, besides scalar and gauge fields coming from the Ramond-Ramond sector. The reduction to four dimensions brings to scene moduli fields. We generalize this effective action by introducing two arbitrary parameters, {omega} and m, connected with the dilaton and axion couplings. In this way, more general frameworks can be analyzed. Regular solutions with a bounce can be obtained for a range of (negative) values of the parameter {omega} which, however, exclude the pure string configuration ({omega}=-1). We study the evolution of scalar perturbations in such cosmological scenarios. The predicted primordial power spectrum decreases with the wave number with spectral index n{sub s}=-2, in contradiction with the results of the Wilkinson microwave anisotropy probe (WMAP). Hence, all such effective string motivated cosmological bouncing models seem to be ruled out, at least at the tree level approximation.

Loop quantization of a model for D = 1 + 2 (anti)de Sitter gravity coupled to topological matter

Abstract.We present a complete classification, at the classical level, of the observables of topological Yang-Mills theories with an extended shift supersymmetry of N generators, in any space-time dimension. The observables are defined as the Yang-Mills BRST cohomology classes of shift supersymmetry invariants. These cohomology classes turn out to be solutions of an N-extension of Wittens equivariant cohomology. This work generalizes results known in the case of shift supersymmetry with a single generator.