Dualities in Supergravity and Solvable Lie Algebras

Abstract

The purpose of the present thesis is to give a self-contained review of the solvable Lie algebra approach to supergravity problems related with S, T and U dualities. After recalling the general features of dualities in both Superstring theory and Supergravity, we introduce the solvable Lie algebra formalism as an alternative description of the scalar manifold in a broad class of supergravity theories. It is emphasized how this mathematical technique on one hand allows to achieve a geometrical intrinsic characterization of Ramond-Ramond, Neveu-Schwarz and Peccei-Quinn scalars, once the supergravity theory is interpreted as the low energy limit of a suitably compactified superstring theory, on the other hand provides a convenient framework in which to deal with several non-perturbative problems. Using solvable Lie algebras for instance we find a general mechanism for spontaneous N=2 to N=1 local supersymmetry breaking. Moreover solvable Lie algebras are used to define a general method for studying systematically BPS saturated Black Hole solutions in supergravity.

PhD thesis, 142 pages, 1 Textype, 14 eps-figures

References in corpus (15)

• String Solitons
• Strong-Weak Coupling Duality in Four Dimensional String Theory
• Four Dimensional String/String/String Triality
• Black Holes in String Theory
• Spontaneous Breaking of N=2 Global Supersymmetry
• Summing up D-Instantons
• Classical and quantum N=2 supersymmetric black holes
• General class of BPS saturated dyonic black holes as exact superstring solutions
• U-Duality and Central Charges in Various Dimensions Revisited
• Spontaneous Breaking of N=2 to N=1 in Rigid and Local Supersymmetric Theories
• Minimal Higgs Branch for the Breaking of Half of the Supersymmetries in N=2 Supergravity
• Large Softly broken N=2 QCD
• A Search for Non-Perturbative Dualities of Local $N=2$ Yang--Mills Theories from Calabi--Yau Threefolds
• On Electromagnetic Duality in Locally Supersymmetric N=2 Yang--Mills Theory
• R-Symmetry and the Topological Twist of N=2 Effective Supergravities of Heterotic Strings