Supersymmetric solutions of gauged five-dimensional supergravity with general matter couplings

We perform the characterization program for the supersymmetric configurations and solutions of the $\mathcal{N}=1$, $d=5$ Supergravity Theory coupled to an arbitrary number of vectors, tensors and hypermultiplets and with general non-Abelian gaugins. By using the conditions yielded by the characterization program, new exact supersymmetric solutions are found in the $SO(4,1)/SO(4)$ model for the hyperscalars and with $SU(2)\times U(1)$ as the gauge group. The solutions also content non-trivial vector and massive tensor fields, the latter being charged under the U(1) sector of the gauge group and with selfdual spatial components. These solutions are black holes with $AdS_2 \times S^3$ near horizon geometry in the gauged version of the theory and for the ungauged case we found naked singularities. We also analyze supersymmetric solutions with only the scalars $\phi^x$ of the vector/tensor multiplets and the metric as the non-trivial fields. We find that only in the null class the scalars $\phi^x$ can be non-constant and for the case of constant $\phi^x$ we refine the classification in terms of the contributions to the scalar potential.Comment: Minor changes in wording and some typos corrected. Version to appear in Class. Quantum Grav. 38 page

Lectures on on Black Holes, Topological Strings and Quantum Attractors (2.0)

In these lecture notes, we review some recent developments on the relation between the macroscopic entropy of four-dimensional BPS black holes and the microscopic counting of states, beyond the thermodynamical, large charge limit. After a brief overview of charged black holes in supergravity and string theory, we give an extensive introduction to special and very special geometry, attractor flows and topological string theory, including holomorphic anomalies. We then expose the Ooguri-Strominger-Vafa (OSV) conjecture which relates microscopic degeneracies to the topological string amplitude, and review precision tests of this formula on ``small'' black holes. Finally, motivated by a holographic interpretation of the OSV conjecture, we give a systematic approach to the radial quantization of BPS black holes (i.e. quantum attractors). This suggests the existence of a one-parameter generalization of the topological string amplitude, and provides a general framework for constructing automorphic partition functions for black hole degeneracies in theories with sufficient degree of symmetry.Comment: 103 pages, 8 figures, 21 exercises, uses JHEP3.cls; v5: important upgrade, prepared for the proceedings of Frascati School on Attractor Mechanism; Sec 7 was largely rewritten to incorporate recent progress; more figures, more refs, and minor changes in abstract and introductio