Transformation of Black-Hole Hair under Duality and Supersymmetry

We study the transformation under the String Theory duality group of the observable charges (mass, angular momentum, NUT charge, electric, magnetic and different scalar charges) of four dimensional point-like objects whose asymptotic behavior constitutes a subclass closed under duality. The charges fall into two complex four-dimensional representations of the duality group. T duality (including Buscher's) has an O(1,2) action on them and S duality a U(1) action. The generalized Bogomol'nyi bound is an U(2,2)-invariant built out of one representations while the other representation (which includes the angular momentum) never appears in it. The bound is manifestly duality-invariant. Consistency between T duality and supersymmetry requires that primary scalar hair is included in the Bogomol'nyi bound. Four-dimensional supersymmetric massless black holes are the T duals in time of massive supersymmetric black holes. Non-extreme massless ``black holes'' are the T duals of the non-extreme black holes and have primary scalar hair and naked singularities.Comment: LateX file, 48 page

N=2 Einstein-Yang-Mills's BPS solutions

We find the general form of all the supersymmetric configurations and solutions of N=2,d=4 Einstein-Yang-Mills theories. In the timelike case, which we study in great detail, giving many examples, the solutions to the full supergravity equations can be constructed from known flat spacetime solutions of the Bogomol'nyi equations. This allows the regular supersymmetric embedding in supergravity of regular monopole solutions ('t Hooft-Poyakov's, Weinberg's, Wilkinson and Bais's) but also embeddings of irregular solutions to the Bogomol'nyi equations which turn out to be regular black holes with different forms of non-Abelian hair once the non-triviality of the spacetime metric is taken into account. The attractor mechanism is realized in a gauge-covariant way. In the null case we determine the general equations that supersymmetric configurations and solutions must satisfy but we do not find relevant new supersymmetric solutions.Comment: latex2e, 53 pages, 2 figure

N=2 Einstein-Yang-Mills' static two-center solutions

We construct bona fide one- and two-center supersymmetric solutions to N=2, d=4 supergravity coupled to SU(2) non-Abelian vector multiplets. The solutions describe black holes and global monopoles alone or in equilibrium with each other and exhibit non-Abelian hairs of different kinds.Comment: 46 pages, 1 figure; v2 references adde

Resolution of SU(2) monopole singularities by oxidation

We show how "colored" SU(2) BPS monopoles (that is: SU(2) monopoles satisfying the Bogomol'nyi equation whose Higgs field and magnetic charge vanish at infinity and which are singular at the origin) can be obtained from the BPST instanton by a singular dimensional reduction, explaining the origin of the singularity and implying that the singularity can be cured by the oxidation of the solution. We study the oxidation of other monopole solutions in this scheme.Comment: 13 pages, LaTeX file, no figure

Non-Abelian black holes in string theory

We study a family of 5-dimensional non-Abelian black holes that can be obtained by adding an instanton field to the well-known D1D5W Abelian black holes. Naively, the non-Abelian fields seem to contribute to the black-hole entropy but not to the mass due to their rapid fall-off at spatial infinity. By uplifting the 5-dimensional supergravity solution to 10-dimensional Heterotic Supergravity first and then dualizing it into a Type-I Supergravity solution, we show that the non-Abelian fields are associated to D5-branes dissolved into the D9-branes (dual to the Heterotic "gauge 5-branes") and that their associated RR charge does not, in fact, contribute to the entropy, which only depends on the number16 pages of D-strings and D5 branes and the momentum along the D-strings, as in the Abelian case. These "dissolved" or "gauge" D5-branes do contribute to the mass in the expected form. The correct interpretation of the 5-dimensional charges in terms of the string-theory objects solves the non-Abelian hair puzzle, allowing for the microscopic accounting of the entropy. We discuss the validity of the solution when alpha prime corrections are taken into account.Comment: Latex 2e file, 21 pages. A full appendix on alpha prime corrections and the corresponding discussions have been added. The conclusions have suffered minor changes. Version accepted in JHE

Supersymmetric Brane-Worlds

We present warped metrics which solve Einstein equations with arbitrary cosmological constants in both in upper and lower dimensions. When the lower-dimensional metric is the maximally symmetric one compatible with the chosen value of the cosmological constant, the upper-dimensional metric is also the maximally symmetric one and there is maximal unbroken supersymmetry as well. We then introduce brane sources and find solutions with analogous properties, except for supersymmetry, which is generically broken in the orbifolding procedure (one half is preserved in two special cases), and analyze metric perturbations in these backgrounds In analogy with the D8-brane we propose an effective $(\hat{d}-2)$-brane action which acts as a source for the RS solution. The action consists of a Nambu-Goto piece and a Wess-Zumino term containing a $(\hat{d}-1)$-form field. It has the standard form of the action for a BPS extended object, in correspondence with the supersymmetry preserved by the solution.Comment: 13 pages, Latex2e. Corrected and shortened version to appear in Phys. Lett.

Black hole chemistry, the cosmological constant and the embedding tensor

We study black-hole thermodynamics in theories that contain dimensionful constants such as the cosmological constant or coupling constants in Wald's formalism. The most natural way to deal with these constants is to promote them to scalar fields introducing a (d-1)-form Lagrange multiplier that forces them to be constant on-shell. These (d-1)-form potentials provide a dual description of them and, in the context of superstring/supergravity theories, a higher-dimensional origin/explanation. In the context of gauged supergravity theories, all these constants can be collected in the embedding tensor. We show in an explicit 4-dimensional example that the embedding tensor can also be understood as a thermodynamical variable that occurs in the Smarr formula in a duality-invariant fashion. This establishes an interesting link between black-hole thermodynamics, gaugings and compactifications in the context of superstring/supergravity theories.Comment: References added, 43 pages, no figure