Supersymmetric black holes and attractors in gauged supergravity with hypermultiplets

We consider four-dimensional $N=2$ supergravity coupled to vector- and hypermultiplets, where abelian isometries of the quaternionic K\"ahler hypermultiplet scalar manifold are gauged. Using the recipe given by Meessen and Ort\'{\i}n in arXiv:1204.0493, we analytically construct a supersymmetric black hole solution for the case of just one vector multiplet with prepotential ${\cal F}=-i\chi^0\chi^1$, and the universal hypermultiplet. This solution has a running dilaton, and it interpolates between $\text{AdS}_2\times\text{H}^2$ at the horizon and a hyperscaling-violating type geometry at infinity, conformal to $\text{AdS}_2\times\text{H}^2$. It carries two magnetic charges that are completely fixed in terms of the parameters that appear in the Killing vector used for the gauging. In the second part of the paper, we extend the work of Bellucci et al. on black hole attractors in gauged supergravity to the case where also hypermultiplets are present. The attractors are shown to be governed by an effective potential $V_{\text{eff}}$, which is extremized on the horizon by all the scalar fields of the theory. Moreover, the entropy is given by the critical value of $V_{\text{eff}}$. In the limit of vanishing scalar potential, $V_{\text{eff}}$ reduces (up to a prefactor) to the usual black hole potential.Comment: 21 pages, uses jheppub.sty. v2: Refs. adde

BPS black holes in a non-homogeneous deformation of the stu model of N=2N=2, D=4D=4 gauged supergravity

We consider a deformation of the well-known stu model of $N=2$, $D=4$ supergravity, characterized by a non-homogeneous special K\"{a}hler manifold, and by the smallest electric-magnetic duality Lie algebra consistent with its upliftability to five dimensions. We explicitly solve the BPS attractor equations and construct static supersymmetric black holes with radial symmetry, in the context of $\text{U}(1)$ dyonic Fayet-Iliopoulos gauging, focussing on axion-free solutions. Due to non-homogeneity of the scalar manifold, the model evades the analysis recently given in the literature. The relevant physical properties of the resulting black hole solution are discussed.Comment: 26 pages, uses jheppub.st

AdS3_3 solutions with exceptional supersymmetry

Among the possible superalgebras that contain the AdS$_3$ isometries, two interesting possibilities are the exceptional $F(4)$ and $G(3)$. Their R-symmetry is respectively SO(7) and $G_2$, and the amount of supersymmetry ${\cal N}=8$ and ${\cal N}=7$. We find that there exist two (locally) unique solutions in type IIA supergravity that realize these superalgebras, and we provide their analytic expressions. In both cases, the internal space is obtained by a round six-sphere fibred over an interval, with an O8-plane at one end. The R-symmetry is the symmetry group of the sphere; in the $G(3)$ case, it is broken to $G_2$ by fluxes. We also find several numerical ${\cal N}=1$ solutions with $G_2$ flavor symmetry, with various localized sources, including O2-planes and O8-planes.Comment: 30 pages, 4 figures; v3: revised appendix, minor correction

Towards AdS Distances in String Theory

The AdS Distance Conjecture proposes to assign a notion of distance between AdS vacua in quantum gravity. We perform some initial developments of this idea. We first propose more sharply how to define a metric on conformal variations of AdS through the action. This metric is negative, making the distance ill-defined, a property relating to the famous conformal factor problem of quantum gravity. However, in string theory, variations of the AdS conformal factor are accompanied by variations of the internal dimensions and of the background flux. We propose an $\textit{action metric}$, which accounts for all of these variations simultaneously. Accounting for the variations of the overall volume of the internal dimensions can flip the sign of the action metric making it positive. This positivity is related to the absence of scale separation between the internal and external dimensions: the negative external conformal contribution must be sub-dominant to the positive internal contribution. We then focus specifically on the families of solutions of eleven-dimensional supergravity on AdS$_4 \times S^7$ and AdS$_7 \times S^4$. For these, there is only a single further additional contribution to the action metric coming from variations of the Freund-Rubin flux. This contribution is subtle to implement, and the unique prescription we find requires singling out the radial direction of AdS as special. Adding the flux contribution yields an overall total action metric which becomes positive for both the AdS$_4$ and AdS$_7$ families of solutions. The final result is therefore a procedure which yields a well-defined distance for these families of solutions.Comment: 30 page

Black string first order flow in N = 2, d = 5 abelian gauged supergravity

We derive both BPS and non-BPS first-order flow equations for magnetically charged black strings in five-dimensional N=2 abelian gauged supergravity, using the Hamilton-Jacobi formalism. This is first done for the coupling to vector multiplets only and U(1) Fayet-Iliopoulos (FI) gauging, and then generalized to the case where also hypermultiplets are present, and abelian symmetries of the quaternionic hyperscalar target space are gauged. We then use these results to derive the attractor equations for near-horizon geometries of extremal black strings, and solve them explicitely for the case where the constants appearing in the Chern-Simons term of the supergravity action satisfy an adjoint identity. This allows to compute in generality the central charge of the two-dimensional conformal field theory that describes the black strings in the infrared, in terms of the magnetic charges, the CY intersection numbers and the FI constants. Finally, we extend the r-map to gauged supergravity and use it to relate our flow equations to those in four dimensions.Comment: 21 pages, uses jheppub.sty. v2: Minor errors corrected, refs. added. v3: Minor error corrected in app. B, small discussion of string theory realization added in final remark

AdS2_2 near-horizons, defects and string dualities

We construct a new family of $\text{AdS}_2\times S^3\times S^2$ solutions to Type IIB supergravity arising as near-horizon geometries of D1-F1-D3-D5-NS5-D7 brane intersections preserving 4 supersymmetries. We show that a subclass of these solutions asymptotes locally to the $\text{AdS}_6\times S^2\times \Sigma_2$ solution to Type IIB supergravity holographically dual to the five dimensional Sp(N) fixed point theory. This suggests that these solutions can be interpreted as D1-F1-D3 line defects within this CFT. Switching off the D7-branes, we act with $\text{SL}(2, \mathbb{R})$ to construct a second family of solutions that can be related to an $\text{AdS}_3\times S^3\times S^3$ class of M-theory backgrounds describing surface defects within the six dimensional (1,0) SCFT dual to $\text{AdS}_7/\mathbb{Z}_k\times S^4$. Finally, using non-Abelian T-duality we construct new classes of $\text{AdS}_2\times S^2\times S^2$ solutions to Type IIA supergravity with 4 supercharges and elaborate on their M-theory origin.Comment: 24 page