D=11 Supermembrane wrapped on calibrated submanifolds

We construct the Hamiltonian of the D=11 Supermembrane with topological conditions on configuration space. It may be interpreted as a supermembrane theory where all configurations are wrapped in an irreducible way on a calibrated submanifold of a compact sector of the target space. We prove that the spectrum of its Hamiltonian is discrete with finite multiplicity. The construction is explicitly perfomed for a compact sector of the target space being a $2g$ dimensional flat torus and the base manifold of the Supermembrane a genus $g$ compact Riemann surface. The topological conditions on configuration space work in such a way that the $g=2$ case may be interpreted as the intersection of two D=11 Supermembranes over $g=1$ surfaces, with their corresponding topological conditions. The discreteness of the spectrum is preserved by the intersection procedure. Between the configurations satisfying the topological conditions there are minimal configurations which describe minimal immersions from the base manifold to the compact sector of the target space. They allow to map the D=11 Supermembrane with topological conditions to a symplectic noncommutative Yang-Mills theory. We analyze geometrical properties of these configurations in the context of Supermembranes and D-branes theories. We show that this class of configurations also minimizes the Hamiltonian of D-branes theories.Comment: 24 page

The Tensor Hierarchies of Pure N=2,d=4,5,6 Supergravities

We study the supersymmetric tensor hierarchy of pure (gauged) N=2,d=4,5,6 supergravity and compare them with those of the pure, ungauged, theories (worked out by Gomis and Roest for d=5) and the predictions of the Kac-Moody approach made by Kleinschmidt and Roest. We find complete agreement in the ungauged case but we also find that, after gauging, new Stueckelberg symmetries reduce the number of independent "physical" top-forms. The analysis has to be performed to all orders in fermion fields. We discuss the construction of the worldvolume effective actions for the p-branes which are charged with respect to the (p+1)-form potentials and the relations between the tensor hierarchies and p-branes upon dimensional reduction.Comment: LaTeX2e file, 20 pages, 1 figure Results refined by extension of the analysis to all orders in fermion

All the timelike supersymmetric solutions of all ungauged d=4 supergravities

We determine the form of all timelike supersymmetric solutions of all N greater or equal than 2, d=4 ungauged supergravities, for N less or equal than 4 coupled to vector supermultiplets, using the $Usp(n+1,n+1)-symmetric formulation of Andrianopoli, D'Auria and Ferrara and the spinor-bilinears method, while preserving the global symmetries of the theories all the way. As previously conjectured in the literature, the supersymmetric solutions are always associated to a truncation to an N=2 theory that may include hypermultiplets, although fields which are eliminated in the truncations can have non-trivial values, as is required by the preservation of the global symmetry of the theories. The solutions are determined by a number of independent functions, harmonic in transverse space, which is twice the number of vector fields of the theory (n+1). The transverse space is flat if an only if the would-be hyperscalars of the associated N=2 truncation are trivial.Comment: v3: Some changes in the introduction. Version to be published in JHE

The supersymmetric solutions and extensions of ungauged matter-coupled N=1,d=4 supergravity

We find the most general supersymmetric solutions of ungauged N=1,d=4 supergravity coupled to an arbitrary number of vector and chiral supermultiplets, which turn out to be essentially pp-waves and strings. We also introduce magnetic 1-forms and their supersymmetry transformations and 2-forms associated to the isometries of the scalar manifold and their supersymmetry transformations. Only the latter can couple to BPS objects (strings), in agreement with our results.Comment: Some misprints and citations correcte

Solitons and instantons in vacuum stability

We investigate the instanton solutions and soliton-like bubbles in vacuum dynamics. We show that the results of recent CERN experiments lead to the fact that our vacuum is safe. We present a new mechanism, where the space-time dimension plays an important role, that explains why our Universe is stable. We provide new evidence that supports a process for the origin of Matter-Antimatter Asymmetry recently introduced by other scientists. We examine confinement in the context of escape problems. We discuss multiverse, string theory landscape, and extra-dimensions using our framework. We use our solutions to introduce some hypotheses about Dark Matter and Dark Energy

Characterization of all the supersymmetric solutions of gauged N=1,d=5 supergravity

We find a complete characterization of all the supersymmetric solutions of non-Abelian gauged N=1,d=5 supergravity coupled to vector multiplets and hypermultiplets: the generic forms of the metrics as functions of the scalars and vector fields plus the equations that all these must satisfy. These equations are now a complicated non-linear system and there it seems impossible to produce an algorithm to construct systematically all supersymmetric solutions.Comment: Some references and two comments adde

Black holes and black strings of N=2, d=5 supergravity in the H-FGK formalism

We study general classes and properties of extremal and non-extremal static black-hole solutions of N=2, d=5 supergravity coupled to vector multiplets using the recently proposed H-FGK formalism, which we also extend to static black strings. We explain how to determine the integration constants and physical parameters of the black-hole and black-string solutions. We derive some model-independent statements, including the transformation of non-extremal flow equations to the form of those for the extremal flow. We apply our methods to the construction of example solutions (among others a new extremal string solution of heterotic string theory on K_3 \times S^1). In the cases where we have calculated it explicitly, the product of areas of the inner and outer horizon of a non-extremal solution coincides with the square of the moduli-independent area of the horizon of the extremal solution with the same charges.Comment: 33 pages. Revised version: references added. No other change

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