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**1 - 4**of**4**### IFT-UAM/CSIC-13-107 The violation of the No-Hair Conjecture infour-dimensional ungauged Supergravity

"... By choosing a particular, String Theory inspired, Special Kähler manifold, we are able to finda N = 2 four-dimensional ungauged Supergravity model that contains supersymmetric blackhole solutions that violate the folk uniqueness theorems that are expected to hold in ungaugedSupergravity. The black h ..."

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By choosing a particular, String Theory inspired, Special Kähler manifold, we are able to finda N = 2 four-dimensional ungauged Supergravity model that contains supersymmetric blackhole solutions that violate the folk uniqueness theorems that are expected to hold in ungaugedSupergravity. The black hole solutions are regular in the sense that they have a positive mass anda unique physical singularity hidden by an event horizon. In contradistinction to most examplesalready known in the literature, we find our solutions in a theory without scalar potential, gaugingsor higher order curvature terms. 1 ar X iv

### Half-flat Quantum Hair

"... By wrapping D3-branes over 3-cycles on a half-flat manifold we construct an effec-tive supersymmetric black hole in the N = 2 low-energy theory in four-dimensions. Specifically we find that the torsion cycles present in a half-flat compactification, corresponding to the mirror symmetric image of ele ..."

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By wrapping D3-branes over 3-cycles on a half-flat manifold we construct an effec-tive supersymmetric black hole in the N = 2 low-energy theory in four-dimensions. Specifically we find that the torsion cycles present in a half-flat compactification, corresponding to the mirror symmetric image of electric NS flux on a Calabi-Yau manifold, manifest in the half-flat black hole as quantum hair. We compute the electric and magnetic charges related to the quantum hair, and also the mass contribution to the effective black hole. We find that by wrapping a number of D3-branes equal to the order of the discrete group associated to the torsional part of the half-flat homology, the effective charge and mass terms vanishes. We compute the variation of entropy and the corresponding temperature associated with the lost of quantum hair. We also comment on the equivalence between canceling Freed-Witten anomaly and the assumption of self-duality for the 5-form field strength. Finally from a K-theoretical perspective, we compute the presence of discrete RR charge of D-branes wrapping torsional cycles in a half-flat manifold.