First order flow equations for nonextremal black holes in AdS (super)gravity

We consider electrically charged static nonextremal black holes in $d$-dimensional Einstein-Maxwell-(A)dS gravity, whose horizon is a generic Einstein space in $d-2$ dimensions. It is shown that for this system the Hamilton-Jacobi equation is exactly solvable and admits two branches of solutions. One of them exhibits a non-simply connected domain of integration constants and does not reduce to the well-known solution for the $d=4$ BPS case. The principal functions generate two first order flows that are analytically different, but support the same general solution. One of the two sets of flow equations corresponds to those found by L\"u, Pope and V\'azquez-Poritz in hep-th/0307001 and (for $d=4$ and $\Lambda=0$) by Miller, Schalm and Weinberg in hep-th/0612308. This clarifies also the reason for the very existence of first order equations for nonextremal black holes, namely, they are just the expressions for the conjugate momenta in terms of derivatives of the principal function in a Hamilton-Jacobi formalism. In the last part of our paper we analyze how much of these integrability properties generalizes to matter-coupled $N=2$, $d=4$ gauged supergravity.Comment: 17 pages. v2: Refs. added. v3: Final version to appear in JHE

On the integrability of Einstein-Maxwell-(A)dS gravity in presence of Killing vectors

We study some symmetry and integrability properties of four-dimensional Einstein-Maxwell gravity with nonvanishing cosmological constant in the presence of Killing vectors. First of all, we consider stationary spacetimes, which lead, after a timelike Kaluza-Klein reduction followed by a dualization of the two vector fields, to a three-dimensional nonlinear sigma model coupled to gravity, whose target space is a noncompact version of $\mathbb{C}\text{P}^2$ with SU(2,1) isometry group. It is shown that the potential for the scalars, that arises from the cosmological constant in four dimensions, breaks three of the eight SU(2,1) symmetries, corresponding to the generalized Ehlers and the two Harrison transformations. This leaves a semidirect product of a one-dimensional Heisenberg group and a translation group $\mathbb{R}^2$ as residual symmetry. We show that, under the additional assumptions that the three-dimensional manifold is conformal to a product space $\mathbb{R}\times\Sigma$, and all fields depend only on the coordinate along $\mathbb{R}$, the equations of motion are integrable. This generalizes the results of Leigh et al. in arXiv:1403.6511 to the case where also electromagnetic fields are present. In the second part of the paper we consider the purely gravitational spacetime admitting a second Killing vector that commutes with the timelike one. We write down the resulting two-dimensional action and discuss its symmetries. If the fields depend only on one of the two coordinates, the equations of motion are again integrable, and the solution turns out to be one constructed by Krasinski many years ago.Comment: 24 pages, uses jheppub.sty. v2: Final version to be published in CQ

Duality invariance in Fayet-Iliopoulos gauged supergravity

We propose a geometric method to study the residual symmetries in $N=2$, $d=4$ $\text{U}(1)$ Fayet-Iliopoulos (FI) gauged supergravity. It essentially involves the stabilization of the symplectic vector of gauge couplings (FI parameters) under the action of the U-duality symmetry of the ungauged theory. In particular we are interested in those transformations that act non-trivially on the solutions and produce scalar hair and dyonic black holes from a given seed. We illustrate the procedure for finding this group in general and then show how it works in some specific models. For the prepotential $F=-iX^0X^1$, we use our method to add one more parameter to the rotating Chow-Comp\`ere solution, representing scalar hair.Comment: 31 pages, uses jheppub.sty. Final version to appear on JHE

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

“High performance” work practices, decentralization, and profitability: evidence from panel data -super-†

The aim of this article is to test the effects on firm profitability of the adoption of both “high performance” work practices (HPWPs) and changes in organizational design relating to the depth of the corporate hierarchy and the allocation of decision authority. For this purpose, we resort to panel estimates based on a longitudinal data set that includes information relating to 109 Italian manufacturing single-plant firms observed in the 1990s during 7 years. The econometric results show that the adoption of HPWPs leads to better performances, especially when it is associated with the delegation of decision authority downward the corporate hierarchy. Copyright 2007 , Oxford University Press.

Nonlinear symmetries of black hole entropy in gauged supergravity

Abstract Freudenthal duality in N = 2, D = 4 ungauged supergravity is generated by an anti-involutive operator that acts on the electromagnetic fluxes, and results to be a symmetry of the Bekenstein-Hawking entropy. We show that, with a suitable extension, this duality can be generalized to the abelian gauged case as well, even in presence of hypermultiplets. By defining Freudenthal duality along the scalar flow, one can prove that two configurations of charges and gaugings linked by the Freudenthal operator share the same set of values of the scalar fields at the black hole horizon. Consequently, Freudenthal duality is promoted to a nonlinear symmetry of the black hole entropy. We explicitly show this invariance for the model with prepotential F = −iX 0 X 1 and Fayet-Iliopoulos gauging

Maxillary extrafollicular adenomatoid odontogenic tumor: root resorption and involvement of the maxillary sinus and nasal cavity

Adenomatoid odontogenic tumor (AOT) is a benign, slow-growing lesion and it is considered the fourth most common odontogenic tumor. AOT affects more frequently the young subjects with a predilection for the second and third decades of life. We present here the case of a 36-year-old man affected by large extrafollicular AOT which caused roots resorption of multiple teeth. The lesion involved the entire right maxillary bone and extended into the right maxillary sinus up to the orbital floor and the nasal cavity. Intra-oral surgical excision of the AOT and functional endoscopic sinus surgery led to complete clinical healing in absence of local recurrences