Pursuing Gravitational S-Duality

Recently a strong-weak coupling duality in non-abelian non-supersymmetric theories in four dimensions has been found. An analogous procedure is reviewed, which allows to find the `dual action' to the gauge theory of dynamical gravity constructed by the MacDowell-Mansouri model plus the superposition of a $\Theta$ term.Comment: Invited paper to appear in the special issue of the `Journal of Chaos, Solitons and Fractals' on: "Superstrings, M,F,S,... Theory" (M.S. El Naschie and C. Castro, editors), 19 pages, LaTeX file, no figure

Gravitational Duality in MacDowell-Mansouri Gauge Theory

Strong-weak duality invariance can only be defined for particular sectors of supersymmetric Yang-Mills theories. Nevertheless, for full non-Abelian non-supersymmetric theories, dual theories with inverted couplings, have been found. We show that an analogous procedure allows to find the dual action to the gauge theory of gravity constructed by the MacDowell-Mansouri model plus the superposition of a $\Theta$ term.Comment: 9 pages, LaTeX, no figure

Avoiding degenerate coframes in an affine gauge approach to quantum gravity

In quantum models of gravity, it is surmized that configurations with degenerate coframes could occur during topology change of the underlying spacetime structure. However, the coframe is not the true Yang--Mills type gauge field of the translations, since it lacks the inhomogeneous gradient term in the gauge transformations. By explicitly restoring this ``hidden" piece within the framework of the affine gauge approach to gravity, one can avoid the metric or coframe degeneracy which would otherwise interfere with the integrations within the path integral. This is an important advantage for quantization.Comment: 14 pages, Preprint Cologne-thp-1993-H

Self-dual gravity and self-dual Yang-Mills in the context of Macdowell-Mansouri formalism

In this work we propose an action which unifies self-dual gravity and self-dual Yang-Mills in the context of the Macdowell-Mansouri formalism. We claim that such an action may be used to find the S-dual action for both self-dual gravity and self-dual Yang-Mills.Comment: 8 pages, Revtex, no figures, submitted to Phys. Rev.

Remarks on 2+1 Self-dual Chern-Simons Gravity

We study 2+1 Chern-Simons gravity at the classical action level. In particular we rederive the linear combinations of the ``standard'' and ``exotic'' Einstein actions, from the (anti) self-duality of the ``internal'' Lorentzian indices. The relation to a genuine four-dimensional (anti)self-dual topological theory greatly facilitates the analysis and its relation to hyperbolic three-dimensional geometry. Finally a non-abelian vector field ``dual'' action is also obtained.Comment: 16+1 pages, LaTeX file, no figures, clarifications and comments added, typos corrected and one reference adde

Large-scale unit commitment under uncertainty: an updated literature survey

The Unit Commitment problem in energy management aims at finding the optimal production schedule of a set of generation units, while meeting various system-wide constraints. It has always been a large-scale, non-convex, difficult problem, especially in view of the fact that, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focussing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper "Large-scale Unit Commitment under uncertainty: a literature survey" that appeared in 4OR 13(2), 115--171 (2015); this version has over 170 more citations, most of which appeared in the last three years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject

The Gauge Theory of the de-Sitter Group and Ashtekar Formulation

By adding the Pontrjagin topological invariant to the gauge theory of the de Sitter group proposed by MacDowell and Mansouri we obtain an action quadratic in the field-strengths, of the Chern-Simons type, from which the Ashtekar formulation is derived.Comment: 9 page