On new maximal supergravity and its BPS domain-walls

We revise the SU(3)-invariant sector of $\mathcal{N}=8$ supergravity with dyonic SO(8) gaugings. By using the embedding tensor formalism, analytic expressions for the scalar potential, superpotential(s) and fermion mass terms are obtained as a function of the electromagnetic phase $\omega$ and the scalars in the theory. Equipped with these results, we explore non-supersymmetric AdS critical points at $\omega \neq 0$ for which perturbative stability could not be analysed before. The $\omega$-dependent superpotential is then used to derive first-order flow equations and obtain new BPS domain-wall solutions at $\omega \neq 0$. We numerically look at steepest-descent paths motivated by the (conjectured) RG flows.Comment: 40 pages (30 pages + appendices), 3 tables, 6 figures. v2: References added and discussion in section 4.2 clarified. v3: References added, published version. v4: Fixed typo

BPS black hole horizons from massive IIA

The maximal four-dimensional supergravity with a dyonic ISO(7) gauging that arises from the reduction of massive IIA on a six-sphere has recently been shown to accommodate static BPS black holes with hyperbolic horizons. When restricted to the N=2 subsector that retains one vector multiplet and the universal hypermultiplet, the attractor mechanism was shown to fix both the vector charges and the scalar fields at the horizon to a unique configuration in terms of the gauging parameters. In order to assess the (non-)uniqueness of BPS black hole horizons from massive IIA, we extend the study of the attractor mechanism to other N=2 subsectors including additional matter multiplets. We note that, while extending the hypermultiplet sector does not modify the set of solutions to the attractor equations, the inclusion of additional vector multiplets results in new hyperbolic/spherical horizons containing free parameters. The model with three vector multiplets and the universal hypermultiplet, which is the massive IIA analogue of the STU-model from M-theory, may play a relevant role in massive IIA holography.Comment: 18 pages, 2 figures. v2: typos fixed, notation and presentation improved, references added. v3: published versio

Vector fields, separatrices and Kato surfaces

We prove that a singular complex surface that admits a complete holomorphic vector field that has no invariant curve through a singular point of the surface is obtained from a Kato surface by contracting some divisor (in particular, it is compact). We also prove that, in a singular Stein surface endowed with a complete holomorphic vector field, a singular point of the surface where the zeroes of the vector field do not accumulate is either a quasihomogeneous or a cyclic quotient singularity. The proofs rely in a combinatorial description of the vector field on a resolution of the singular point based on previous work of Rebelo and the author. With the same tools, we reprove some facts about the classification of compact complex surfaces admitting holomorphic vector fields.Comment: post-referee versio

Hypermultiplet gaugings and supersymmetric solutions from 11D and massive IIA supergravity on H(p,q)^{(p,q)} spaces

Supersymmetric $\,\textrm{AdS}_{4}\,$, $\,\textrm{AdS}_{2} \times \Sigma_{2}\,$ and asymptotically AdS$_{4}$ black hole solutions are studied in the context of non-minimal $\,\mathcal{N}=2\,$ supergravity models involving three vector multiplets (STU-model) and Abelian gaugings of the universal hypermultiplet moduli space. Such models correspond to consistent subsectors of the $\,\textrm{SO}(p,q)\,$ and $\,\textrm{ISO}(p,q)\,$ gauged maximal supergravities that arise from the reduction of 11D and massive IIA supergravity on $\,\textrm{H}^{(p,q)}\,$ spaces down to four dimensions. A unified description of all the models is provided in terms of a square-root prepotential and the gauging of a duality-hidden symmetry pair of the universal hypermultiplet. Some aspects of M-theory and massive IIA holography are mentioned in passing.Comment: 10 pages, 3 tables. v2: Published version. v3: minor edits, added clarification

Simulated and Actual Effects of the Brown Shrimp, Penaeus aztecus, Closure in Mexico

Simulations based on a yield-per-recruit model were performed to analyze the impact ofg rowth overfishing on brown shrimp, Penaeus aztecus, and to assess the effects of a closed season inshore and offshore of the Mexican States of Tamaulipas and Veracruz. Closure of both the inshore and offshore fisheries could enhance cohort yield by more than 300%. Cohon yield enhancement would be only about 60-80% if only the offshore season were closed. The closed season of 1993 gave better results as it covered a larger part of the brown shrimp peak recruitment period. Catch per unit of effort (CPUE) after closure in 1993, compared with 1994, was 2.4 times higher than the mean CPUE of the month. Total annual offshore yield increased 72% in 1993 (3,800 metric tons (t)) and 10% in 1994 (506 t) with respect to the mean annual offshore catch during the 10-year period prior to the 1993 closure. Simulation results could help identify alternatives that permit the coexistence of the inshore and offshore fisheries while maintaining high profitability of the brown shrimp fishery

CSOc_c superpotentials

Motivated by their application to holographic RG flows and hairy black holes in Einstein-scalar systems, we present a collection of superpotentials driving the dynamics of $\mathcal{N}=2$ and $\mathcal{N}=1$ four-dimensional supergravities. These theories arise as consistent truncations of the electric/magnetic families of $\textrm{CSO}(p,q,r)_{c}$ maximal supergravities, with ${p+q+r=8}$, discovered by Dall'Agata et al. The $\mathcal{N}=2$ and $\mathcal{N}=1$ truncations describe $\textrm{SU}(3)$ and $\mathbb{Z}_{2} \times \textrm{SO}(3)$ invariant sectors, respectively, and contain AdS$_4$ solutions preserving $\mathcal{N}=1,2,3,4$ supersymmetry within the full theories, as well as various gauge symmetries. Realisations in terms of non-geometric type IIB as well as geometric massive type IIA backgrounds are also discussed. The aim of this note is to provide easy to handle superpotentials that facilitate the study of gravitational and gauge aspects of the $\textrm{CSO}(p,q,r)_{c}$ maximal supergravities avoiding the technicalities required in their construction.Comment: 10 pages, 1 table. v2: Published versio

Composite Operator Method analysis of the underdoped cuprates puzzle

The microscopical analysis of the unconventional and puzzling physics of the underdoped cuprates, as carried out lately by means of the Composite Operator Method (COM) applied to the 2D Hubbard model, is reviewed and systematized. The 2D Hubbard model has been adopted as it has been considered the minimal model capable to describe the most peculiar features of cuprates held responsible for their anomalous behavior. COM is designed to endorse, since its foundations, the systematic emergence in any SCS of new elementary excitations described by composite operators obeying non-canonical algebras. In this case (underdoped cuprates - 2D Hubbard model), the residual interactions - beyond a 2-pole approximation - between the new elementary electronic excitations, dictated by the strong local Coulomb repulsion and well described by the two Hubbard composite operators, have been treated within the Non Crossing Approximation. Given this recipe and exploiting the few unknowns to enforce the Pauli principle content in the solution, it is possible to qualitatively describe some of the anomalous features of high-Tc cuprate superconductors such as large vs. small Fermi surface dichotomy, Fermi surface deconstruction (appearance of Fermi arcs), nodal vs. anti-nodal physics, pseudogap(s), kinks in the electronic dispersion. The resulting scenario envisages a smooth crossover between an ordinary weakly-interacting metal sustaining weak, short-range antiferromagnetic correlations in the overdoped regime to an unconventional poor metal characterized by very strong, long-but-finite-range antiferromagnetic correlations leading to momentum-selective non-Fermi liquid features as well as to the opening of a pseudogap and to the striking differences between the nodal and the anti-nodal dynamics in the underdoped regime.Comment: 30 PRB pages, 13 figures, 35 panel

The Hubbard model beyond the two-pole approximation: a Composite Operator Method study

Within the framework of the Composite Operator Method, a three-pole solution for the two-dimensional Hubbard model is presented and analyzed in detail. In addition to the two Hubbard operators, the operatorial basis comprises a third operator describing electronic transitions dressed by nearest-neighbor spin fluctuations. These latter, compared to charge and pair fluctuations, are assumed to be preeminent in the region of model-parameter space - small doping, low temperature and large on-site Coulomb repulsion - where one expects strong electronic correlations to dominate the physics of the system. This assumption and the consequent choice for the basic field, as well as the whole analytical approximation framework, have been validated through a comprehensive comparison with data for local and single-particle properties obtained by different numerical methods on varying all model parameters. The results systematically agree, both quantitatively and qualitatively, up to coincide in many cases. Many relevant features of the model, reflected by the numerical data, are exactly caught by the proposed solution and, in particular, the crossover between weak and intermediate-strong correlations as well as the shape of the occupied portion of the dispersion. A comprehensive comparison with other $n$-pole solutions is also reported in order to explore and possibly understand the reasons of such good performance.Comment: 19 pages, 8 figures, 27 panel