Toric Elliptic Fibrations and F-Theory Compactifications

The 102581 flat toric elliptic fibrations over P^2 are identified among the Calabi-Yau hypersurfaces that arise from the 473800776 reflexive 4-dimensional polytopes. In order to analyze their elliptic fibration structure, we describe the precise relation between the lattice polytope and the elliptic fibration. The fiber-divisor-graph is introduced as a way to visualize the embedding of the Kodaira fibers in the ambient toric fiber. In particular in the case of non-split discriminant components, this description is far more accurate than previous studies. The discriminant locus and Kodaria fibers groups of all 102581 elliptic fibrations are computed. The maximal gauge group is SU(27), which would naively be in contradiction with 6-dimensional anomaly cancellation.Comment: 40 pages, 14 figures, 3 table

Flipped SU(5) GUTs from E_8 Singularities in F-theory

In this paper we construct supersymmetric flipped SU(5) GUTs from E_8 singularities in F-theory. We start from an SO(10) singularity unfolded from an E_8 singularity by using an SU(4) spectral cover. To obtain realistic models, we consider (3,1) and (2,2) factorizations of the SU(4) cover. After turning on the massless U(1)_X gauge flux, we obtain the SU(5) X U(1)_X gauge group. Based on the well-studied geometric backgrounds in the literature, we demonstrate several models and discuss their phenomenology.Comment: 46 pages, 23 tables, 1 figure, typos corrected, references added, and new examples presente

F-Theory GUT Vacua on Compact Calabi-Yau Fourfolds

We present compact three-generation F-theory GUT models meeting in particular the constraints of D3-tadpole cancellation and D-term supersymmetry. To this end we explicitly construct elliptically fibered Calabi-Yau fourfolds as complete intersections in a toric ambient space. Toric methods enable us to control the singular geometry of the SU(5) GUT model. The GUT brane wraps a non-generic del Pezzo surface admitting GUT symmetry breaking via hypercharge flux. It is contractible to a curve and we demonstrate the existence of a consistent decoupling limit. We compute the Euler characteristic of the singular Calabi-Yau fourfold to show that our three-generation flux solutions obtained via the spectral cover construction are consistent with D3-tadpole cancellation.Comment: 22+12 pages; v2: minor clarifications on decoupling limi

Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions

[EN] We develop a theory of pseudodifferential operators of infinite order for the global classes S. of ultradifferentiable functions in the sense of Bjorck, following the previous ideas given by Prangoski for ultradifferentiable classes in the sense of Komatsu. We study the composition and the transpose of such operators with symbolic calculus and provide several examples.The first author was partially supported by the project GV Prometeo 2017/102, and the second author by the project MTM2016-76647-P. This article is part of the PhD. Thesis of V. Asensio. The authors are very grateful to the two referees for the careful reading and their suggestions and comments, which improved the paper.Asensio, V.; Jornet Casanova, D. (2019). Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 113(4):3477-3512. https://doi.org/10.1007/s13398-019-00710-8S347735121134Albanese, A.A., Jornet, D., Oliaro, A.: Wave front sets for ultradistribution solutions of linear partial differential operators with coefficients in non-quasianalytic classes. Math. Nachr. 285(4), 411–425 (2012)Björck, G.: Linear partial differential operators and generalized distributions. Ark. Mat. 6, 351–407 (1966)Boiti, C., Jornet, D., Oliaro, A.: Regularity of partial differential operators in ultradifferentiable spaces and Wigner type transforms. J. Math. Anal. Appl. 446(1), 920–944 (2017)Bonet, J., Meise, R., Melikhov, S.N.: A comparison of two different ways to define classes of ultradifferentiable functions. Bull. Belg. Math. Soc. Simon Stevin 14(3), 425–444 (2007)Braun, R.W., Meise, R., Taylor, B.A.: Ultradifferentiable functions and Fourier analysis. Results Math. 17(3–4), 206–237 (1990)Braun, R.W.: An extension of Komatsu’s second structure theorem for ultradistributions. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 40(2), 411–417 (1993)Cappiello, M.: Fourier integral operators of infinite order and applications to SG-hyperbolic equations. Tsukuba J. Math. 28(2), 311–361 (2004)Cappiello, M., Pilipović, S., Prangoski, B.: Parametrices and hypoellipticity for pseudodifferential operators on spaces of tempered ultradistributions. J. Pseudo-Differ. Oper. Appl. 5(4), 491–506 (2014)Fernández, C., Galbis, A., Jornet, D.: $$\omega$$-hypoelliptic differential operators of constant strength. J. Math. Anal. Appl. 297(2), 561–576 (2004). Special issue dedicated to John HorváthFernández, C., Galbis, A., Jornet, D.: Pseudodifferential operators on non-quasianalytic classes of Beurling type. Studia Math. 167(2), 99–131 (2005)Fernández, C., Galbis, A., Jornet, D.: Pseudodifferential operators of Beurling type and the wave front set. J. Math. Anal. Appl. 340(2), 1153–1170 (2008)Hashimoto, S., Morimoto, Y., Matsuzawa, T.: Opérateurs pseudodifférentiels et classes de Gevrey. Commun. Partial Differ. Equ. 8(12), 1277–1289 (1983)Hörmander, L.: Pseudo-differential operators. Commun. Pure Appl. Math. 18, 501–517 (1965)Kohn, J.J., Nirenberg, L.: An algebra of pseudo-differential operators. Commun. Pure Appl. Math. 18, 269–305 (1965)Komatsu, H.: Ultradistributions. I. Structure theorems and a characterization. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 20, 25–105 (1973)Langenbruch, M.: Continuation of Gevrey regularity for solutions of partial differential operators. In Functional analysis (Trier, 1994), pages 249–280. de Gruyter, Berlin (1996)Nicola, F.: Rodino, Luigi: Global pseudo-differential calculus on Euclidean spaces, volume 4 of Pseudo-Differential Operators. Theory and Applications. Birkhäuser Verlag, Basel (2010)Prangoski, B.: Pseudodifferential operators of infinite order in spaces of tempered ultradistributions. J. Pseudo-Differ. Oper. Appl. 4(4), 495–549 (2013)Rodino, L.: Linear partial differential operators in Gevrey spaces. World Scientific Publishing Co., Inc., River Edge (1993)Shubin, M.A.: Pseudodifferential operators and spectral theory. Springer-Verlag, Berlin, second edition. Translated from the 1978 Russian original by Stig I. Andersson (2001)Zanghirati, L.: Pseudodifferential operators of infinite order and Gevrey classes. Ann. Univ. Ferrara Sez. VII (N.S.) 31, 197–219, 1985 (1986

Rational F-Theory GUTs without exotics

We construct F-theory GUT models without exotic matter, leading to the MSSM matter spectrum with potential singlet extensions. The interplay of engineering explicit geometric setups, absence of four-dimensional anomalies, and realistic phenomenology of the couplings places severe constraints on the allowed local models in a given geometry. In constructions based on the spectral cover we find no model satisfying all these requirements. We then provide a survey of models with additional U(1) symmetries arising from rational sections of the elliptic fibration in toric constructions and obtain phenomenologically appealing models based on SU(5) tops. Furthermore we perform a bottom-up exploration beyond the toric section constructions discussed in the literature so far and identify benchmark models passing all our criteria, which can serve as a guideline for future geometric engineering.Comment: 27 Pages, 1 Figur

Discovertebral (Andersson) lesions in severe ankylosing spondylitis: a study using MRI and conventional radiography

The objective of this study is to investigate the prevalence of Andersson lesions (AL) in ankylosing spondylitis (AS) patients who will start anti-tumor necrosis factor (TNF) treatment. Radiographs and magnetic resonance imaging (MRI) of the spine were performed before therapy with anti-TNF. ALs were defined as discovertebral endplate destructions on MRI, associated with bone marrow edema and fat replacement or sclerosis, a decreased signal on T1, enhancement after contrast administration (gadolinium diethylenetriamine pentaacetic acid (Gd-DTPA)), and increased signal on T2 and short tau inversion recovery (STIR). Additionally, conventional radiography showed a fracture line, irregular endplates, and increased sclerosis of adjacent vertebral bodies. Fifty-six AS patients were included, 68% males, mean age of 43 years, and mean disease duration of 11 years. The mean bath ankylosing spondylitis disease activity index was 6.4, and 24% of all patients had ankylosis. Only one patient showed a discovertebral abnormality with bone marrow edema of more than 50% of the vertebral bodies adjacent to the intervertebral disk of T7/T8 and T9/T10, a hypodense signal area on T1, and a high signal on STIR. Irregular endplates were depicted, and T1 after Gd-DTPA demonstrated high signal intensity around the disk margins. However, no fracture line was visible on conventional radiology, and therefore, this case was not considered to be an AL. No AL was detected in our AS patients, who were candidates for anti-TNF treatment. One patient showed a discovertebral abnormality on MRI, without a fracture line on conventional radiology. The relative small proportion of patients with a long-established disease might explain this finding for, particularly, an ankylosed spine is prone to develop an AL

Theories of Reference: What Was the Question?

The new theory of reference has won popularity. However, a number of noted philosophers have also attempted to reply to the critical arguments of Kripke and others, and aimed to vindicate the description theory of reference. Such responses are often based on ingenious novel kinds of descriptions, such as rigidified descriptions, causal descriptions, and metalinguistic descriptions. This prolonged debate raises the doubt whether different parties really have any shared understanding of what the central question of the philosophical theory of reference is: what is the main question to which descriptivism and the causal-historical theory have presented competing answers. One aim of the paper is to clarify this issue. The most influential objections to the new theory of reference are critically reviewed. Special attention is also paid to certain important later advances in the new theory of reference, due to Devitt and others

Wavefunctions and the Point of E8 in F-theory

In F-theory GUTs interactions between fields are typically localised at points of enhanced symmetry in the internal dimensions implying that the coefficient of the associated operator can be studied using a local wavefunctions overlap calculation. Some F-theory SU(5) GUT theories may exhibit a maximum symmetry enhancement at a point to E8, and in this case all the operators of the theory can be associated to the same point. We take initial steps towards the study of operators in such theories. We calculate wavefunctions and their overlaps around a general point of enhancement and establish constraints on the local form of the fluxes. We then apply the general results to a simple model at a point of E8 enhancement and calculate some example operators such as Yukawa couplings and dimension-five couplings that can lead to proton decay.Comment: 46 page

Strong Water Absorption in the Dayside Emission Spectrum of the Planet HD 189733b

Recent observations of the extrasolar planet HD 189733b did not reveal the presence of water in the emission spectrum of the planet. Yet models of such 'Hot Jupiter' planets predict an abundance of atmospheric water vapour. Validating and constraining these models is crucial for understanding the physics and chemistry of planetary atmospheres in extreme environments. Indications of the presence of water in the atmosphere of HD 189733b have recently been found in transmission spectra, where the planet's atmosphere selectively absorbs the light of the parent star, and in broadband photometry. Here we report on the detection of strong water absorption in a high signal-to-noise, mid-infrared emission spectrum of the planet itself. We find both a strong downturn in the flux ratio below 10 microns and discrete spectral features that are characteristic of strong absorption by water vapour. The differences between these and previous observations are significant and admit the possibility that predicted planetary-scale dynamical weather structures might alter the emission spectrum over time. Models that match the observed spectrum and the broadband photometry suggest that heat distribution from the dayside to the night side is weak. Reconciling this with the high night side temperature will require a better understanding of atmospheric circulation or possible additional energy sources.Comment: 11 pages, 1 figure, published in Natur