On the unfolding of the fundamental region in integrals of modular invariant amplitudes

We study generic one-loop (string) amplitudes where an integration over the fundamental region F of the modular group is needed. We show how the known lattice-reduction technique used to unfold F to a more suitable region S can be modified to rearrange generic modular invariant amplitudes. The main aim is to unfold F to the strip and, at the same time, to simplify the form of the integrand when it is a sum over a finite number of terms, like in one-loop amplitudes for closed strings compactified on orbifolds. We give a general formula and a recipe to compute modular invariant amplitudes. As an application of the technique we compute the one-loop vacuum energy \rho_n for a generic \Z_n freely acting orbifold, generalizing the result that this energy is less than zero and drives the system to a tachyonic divergence, and that \rho_nm.Comment: 10 pages, 2 figure

Heterotic SO(32) model building in four dimensions

Four dimensional heterotic SO(32) orbifold models are classified systematically with model building applications in mind. We obtain all Z3, Z7 and Z2N models based on vectorial gauge shifts. The resulting gauge groups are reminiscent of those of type-I model building, as they always take the form SO(2n_0)xU(n_1)x...xU(n_{N-1})xSO(2n_N). The complete twisted spectrum is determined simultaneously for all orbifold models in a parametric way depending on n_0,...,n_N, rather than on a model by model basis. This reveals interesting patterns in the twisted states: They are always built out of vectors and anti--symmetric tensors of the U(n) groups, and either vectors or spinors of the SO(2n) groups. Our results may shed additional light on the S-duality between heterotic and type-I strings in four dimensions. As a spin-off we obtain an SO(10) GUT model with four generations from the Z4 orbifold.Comment: 1+37 pages LaTeX, some typos in table 4 corrected, and we have included some discussion on exceptional shift vectors which ignored in the previous version

Resolutions of C^n/Z_n Orbifolds, their U(1) Bundles, and Applications to String Model Building

We describe blowups of C^n/Z_n orbifolds as complex line bundles over CP^{n-1}. We construct some gauge bundles on these resolutions. Apart from the standard embedding, we describe U(1) bundles and an SU(n-1) bundle. Both blowups and their gauge bundles are given explicitly. We investigate ten dimensional SO(32) super Yang-Mills theory coupled to supergravity on these backgrounds. The integrated Bianchi identity implies that there are only a finite number of U(1) bundle models. We describe how the orbifold gauge shift vector can be read off from the gauge background. In this way we can assert that in the blow down limit these models correspond to heterotic C^2/Z_2 and C^3/Z_3 orbifold models. (Only the Z_3 model with unbroken gauge group SO(32) cannot be reconstructed in blowup without torsion.) This is confirmed by computing the charged chiral spectra on the resolutions. The construction of these blowup models implies that the mismatch between type-I and heterotic models on T^6/Z_3 does not signal a complication of S-duality, but rather a problem of type-I model building itself: The standard type-I orbifold model building only allows for a single model on this orbifold, while the blowup models give five different models in blow down.Comment: 1+27 pages LaTeX, 2 figures, some typos correcte

Flux Stabilization in 6 Dimensions: D-terms and Loop Corrections

We analyse D-terms induced by gauge theory fluxes in the context of 6-dimensional supergravity models. On the one hand, this is arguably the simplest concrete setting in which the controversial idea of `D-term uplifts' can be investigated. On the other hand, it is a very plausible intermediate step on the way from a 10d string theory model to 4d phenomenology. Our specific results include the flux-induced one-loop correction to the scalar potential coming from charged hypermultiplets. Furthermore, we comment on the interplay of gauge theory fluxes and gaugino condensation in the present context, demonstrate explicitly how the D-term arises from the gauging of one of the compactification moduli, and briefly discuss further ingredients that may be required for the construction of a phenomenologically viable model. In particular, we show how the 6d dilaton and volume moduli can be simultaneously stabilized, in the spirit of KKLT, by the combination of an R symmetry twist, a gaugino condensate, and a flux-induced D-term.Comment: 24 pages, 1 figure v2:minor correction

Merging Heterotic Orbifolds and K3 Compactifications with Line Bundles

We clarify the relation between six-dimensional Abelian orbifold compactifications of the heterotic string and smooth heterotic K3 compactifications with line bundles for both SO(32) and E_8 x E_8 gauge groups. The T^4/Z_N cases for N=2,3,4 are treated exhaustively, and for N=6 some examples are given. While all T^4/Z_2 and nearly all T^4/Z_3 models have a simple smooth match involving one line bundle only, this is only true for some T^4/Z_4 and T^4/Z_6 cases. We comment on possible matchings with more than one line bundle for the remaining cases. The matching is provided by comparisons of the massless spectra and their anomalies as well as a field theoretic analysis of the blow-ups.Comment: 49 pages, 1 figure; v2: references adde

Sparticle Spectrum of Large Volume Compactification

We examine the large volume compactification of Type IIB string theory or its F theory limit and the associated supersymmetry breakdown and soft terms. It is crucial to incorporate the loop-induced moduli mixing, originating from radiative corrections to the Kahler potential. We show that in the presence of moduli mixing, soft scalar masses generically receive a D-term contribution of the order of the gravitino mass m_{3/2} when the visible sector cycle is stabilized by the D-term potential of an anomalous U(1) gauge symmetry, while the moduli-mediated gaugino masses and A-parameters tend to be of the order of m_{3/2}/8pi^2. It is noticed also that a too large moduli mixing can destabilize the large volume solution by making it a saddle point.Comment: 29 page

A Z2xZ2 standard model

We present a Z_2 x Z_2 orbifold compactification of the E_8 x E_8 heterotic string which gives rise to the exact chiral MSSM spectrum. The GUT breaking SU(5) to SU(3)_C x SU(2)_L x U(1)_Y is realized by modding out a freely acting symmetry. This ensures precision gauge coupling unification. Further, it allows us to break the GUT group without switching on flux in hypercharge direction, such that the standard model gauge bosons can remain massless when the orbifold singularities are blown up. The model has vacuum configurations with matter parity, a large top Yukawa coupling and other phenomenologically appealing features.Comment: 16 page

Low in‑hospital mortality rate in patients with COVID‑19 receiving thromboprophylaxis: data from the multicentre observational START‑COVID Register

Abstract COVID-19 infection causes respiratory pathology with severe interstitial pneumonia and extra-pulmonary complications; in particular, it may predispose to thromboembolic disease. The current guidelines recommend the use of thromboprophylaxis in patients with COVID-19, however, the optimal heparin dosage treatment is not well-established. We conducted a multicentre, Italian, retrospective, observational study on COVID-19 patients admitted to ordinary wards, to describe clinical characteristic of patients at admission, bleeding and thrombotic events occurring during hospital stay. The strategies used for thromboprophylaxis and its role on patient outcome were, also, described. 1091 patients hospitalized were included in the START-COVID-19 Register. During hospital stay, 769 (70.7%) patients were treated with antithrombotic drugs: low molecular weight heparin (the great majority enoxaparin), fondaparinux, or unfractioned heparin. These patients were more frequently affected by comorbidities, such as hypertension, atrial fibrillation, previous thromboembolism, neurological disease,and cancer with respect to patients who did not receive thromboprophylaxis. During hospital stay, 1.2% patients had a major bleeding event. All patients were treated with antithrombotic drugs; 5.4%, had venous thromboembolism [30.5% deep vein thrombosis (DVT), 66.1% pulmonary embolism (PE), and 3.4% patients had DVT + PE]. In our cohort the mortality rate was 18.3%. Heparin use was independently associated with survival in patients aged ≥ 59 years at multivariable analysis. We confirmed the high mortality rate of COVID-19 in hospitalized patients in ordinary wards. Treatment with antithrombotic drugs is significantly associated with a reduction of mortality rates especially in patients older than 59 years