scholarly journals CP symmetry and symplectic modular invariance

2021 ◽  
Vol 10 (6) ◽  
Author(s):  
Gui-Jun Ding ◽  
Ferruccio Feruglio ◽  
Xiang-Gan Liu

We analyze CP symmetry in symplectic modular-invariant supersymmetric theories. We show that for genus g\ge 3g≥3 the definition of CP is unique, while two independent possibilities are allowed when g\le 2g≤2. We discuss the transformation properties of moduli, matter multiplets and modular forms in the Siegel upper half plane, as well as in invariant subspaces. We identify CP-conserving surfaces in the fundamental domain of moduli space. We make use of all these elements to build a CP and symplectic invariant model of lepton masses and mixing angles, where known data are well reproduced and observable phases are predicted in terms of a minimum number of parameters.

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Gui-Jun Ding ◽  
Ferruccio Feruglio ◽  
Xiang-Gan Liu

Abstract We extend the framework of modular invariant supersymmetric theories to encompass invariance under more general discrete groups Γ, that allow the presence of several moduli and make connection with the theory of automorphic forms. Moduli span a coset space G/K, where G is a Lie group and K is a compact subgroup of G, modded out by Γ. For a general choice of G, K, Γ and a generic matter content, we explicitly construct a minimal Kähler potential and a general superpotential, for both rigid and local $$ \mathcal{N} $$ N = 1 supersymmetric theories. We also specialize our construction to the case G = Sp(2g, ℝ), K = U(g) and Γ = Sp(2g, ℤ), whose automorphic forms are Siegel modular forms. We show how our general theory can be consistently restricted to multi-dimensional regions of the moduli space enjoying residual symmetries. After choosing g = 2, we present several examples of models for lepton and quark masses where Yukawa couplings are Siegel modular forms of level 2.


2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Gui-Jun Ding ◽  
Stephen F. King ◽  
Cai-Chang Li ◽  
Ye-Ling Zhou

Abstract We consider for the first time level 7 modular invariant flavour models where the lepton mixing originates from the breaking of modular symmetry and couplings responsible for lepton masses are modular forms. The latter are decomposed into irreducible multiplets of the finite modular group Γ7, which is isomorphic to PSL(2, Z7), the projective special linear group of two dimensional matrices over the finite Galois field of seven elements, containing 168 elements, sometimes written as PSL2(7) or Σ(168). At weight 2, there are 26 linearly independent modular forms, organised into a triplet, a septet and two octets of Γ7. A full list of modular forms up to weight 8 are provided. Assuming the absence of flavons, the simplest modular-invariant models based on Γ7 are constructed, in which neutrinos gain masses via either the Weinberg operator or the type-I seesaw mechanism, and their predictions compared to experiment.


2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Andrew Beckett ◽  
José Figueroa-O’Farrill

Abstract We calculate the relevant Spencer cohomology of the minimal Poincaré superalgebra in 5 spacetime dimensions and use it to define Killing spinors via a connection on the spinor bundle of a 5-dimensional lorentzian spin manifold. We give a definition of bosonic backgrounds in terms of this data. By imposing constraints on the curvature of the spinor connection, we recover the field equations of minimal (ungauged) 5-dimensional supergravity, but also find a set of field equations for an $$ \mathfrak{sp} $$ sp (1)-valued one-form which we interpret as the bosonic data of a class of rigid supersymmetric theories on curved backgrounds. We define the Killing superalgebra of bosonic backgrounds and show that their existence is implied by the field equations. The maximally supersymmetric backgrounds are characterised and their Killing superalgebras are explicitly described as filtered deformations of the Poincaré superalgebra.


2019 ◽  
Vol 2019 (7) ◽  
Author(s):  
P.P. Novichkov ◽  
J.T. Penedo ◽  
S.T. Petcov ◽  
A.V. Titov

2012 ◽  
Vol 08 (04) ◽  
pp. 963-981 ◽  
Author(s):  
ABDELKRIM EL BASRAOUI ◽  
ABDELLAH SEBBAR

We investigate the notion of equivariant forms as functions on the upper half-plane commuting with the action of a discrete group. We put an emphasis on the rational equivariant forms for a modular subgroup that are parametrized by generalized modular forms. Furthermore, we study this parametrization when the modular subgroup is of genus zero as well as their behavior under the effect of the Schwarz derivative.


2000 ◽  
Vol 11 (08) ◽  
pp. 1027-1055 ◽  
Author(s):  
TOMÁS L. GÓMEZ ◽  
IGNACIO SOLS

Roughly speaking, a conic bundle is a surface, fibered over a curve, such that the fibers are conics (not necessarily smooth). We define stability for conic bundles and construct a moduli space. We prove that (after fixing some invariants) these moduli spaces are irreducible (under some conditions). Conic bundles can be thought of as generalizations of orthogonal bundles on curves. We show that in this particular case our definition of stability agrees with the definition of stability for orthogonal bundles. Finally, in an appendix by I. Mundet i Riera, a Hitchin-Kobayashi correspondence is stated for conic bundles.


2006 ◽  
Vol 49 (4) ◽  
pp. 526-535 ◽  
Author(s):  
So Young Choi

AbstractLet Γ0 be a Fuchsian group of the first kind of genus zero and Γ be a subgroup of Γ0 of finite index of genus zero. We find universal recursive relations giving the qr-series coefficients of j0 by using those of the qhs -series of j, where j is the canonical Hauptmodul for Γ and j0 is a Hauptmodul for Γ0 without zeros on the complex upper half plane (here qℓ := e2πiz/ℓ). We find universal recursive formulas for q-series coefficients of any modular form on in terms of those of the canonical Hauptmodul .


2020 ◽  
Author(s):  
Fabrizio Piana ◽  
Chiara Avataneo ◽  
Luca Barale ◽  
Serena Botta ◽  
Roberto Compagnoni ◽  
...  

<p>For a reliable evaluation of the geo-environmental risk related to the presence of naturally occurring asbestos (NOA) in rocks excavated for large infrastructural projects, a proper procedure has to be followed in order to achieve:</p><p>1) the definition of a detailed geological model, tailored on NOA-related issues;</p><p>2) a representative sampling;</p><p>3) a reliable quantitative determination of asbestos content in rock samples.</p><p>Here we describe the approach followed for the evaluation of the NOA content for the excavation of a complex highway tunnel system (“Gronda di Genova” NW Italy), in NOA-bearing meta-ophiolite rocks. The NOA-oriented geological model has been constrained by the individuation of the main “NOA-related petrofacies” —i.e., classes of rocks with common lithological, structural and NOA content features—, and by the identification of “homogeneous zones” – i.e. geological units into which the NOA petrofacies are distributed. Implementation of Gy’s theory on sampling was used and here described to maintain statistical validity during sample processing from the primary rock sample to the analytical sample. SEM-EDS procedure for the quantitative determination of NOA content was improved with an error analysis delivering the minimum number of fibers to be measured to achieve the best analytical results.</p><p>The obtained results allowed the prediction of the NOA hazard in terms of risk zonation along the tunnel section and for the evaluation of the amount of asbestos-bearing spoil to be excavated and managed.</p>


Blood ◽  
2012 ◽  
Vol 120 (21) ◽  
pp. 4415-4415
Author(s):  
Massimiliano Postorino ◽  
Alessandro Lanti ◽  
Eleonora Fiorelli ◽  
Angelo Salvatore Ferraro ◽  
Oana Marilena Chiru ◽  
...  

Abstract Abstract 4415 BACKGROUND. Autologous stem cell transplantation (ASCT) of PBSCs has become a widely applied treatment for Multiple Mieloma (MM), non- Hodgking's lymphoma (NHL) and Hodgking's lymphoma (HL). Successful engraftment correlates with the number of CD34 hemopoietic progenitors cells infused. However, a part of MM or lymphoma patients (5% to 40%) fail to mobilize adequate numbers of PBSCs and thus cannot undergo to ASCT. The success of PBSCs mobilization is usually assessed by the total number of CD34+ stem cells collected, with a cutoff of 2.0–2.5 ×106 CD34+ cells/kg recipient body weight being considered as a minimum requirement for transplant. Poor mobilization of PBSCs is a major limitation to ASCT. Recently GITMO Working Group worked to define operational criteria for the identification/prediction of the poor mobilizer (PM) patients (Olivieri et al. 2011). Plerixafor, a CXCR4 chemochine antagonist, has been showed to improve significantly PBSC mobilization in PM patients. We present our experience using Plerixafor in PM patients classified according to GITMO criteria. METHODS. Between September 2009 and June 2012, a total of 17 patients (9F-8M) were enrolled. The diagnosis were: 10 MM (5F-5M), 1HL (1M), 6 NHL (4F-2M). The median age was 57 (range 15–66). 7 patients (3MM, 4NHL) were defined “Proven PM” and 10 patients (7MM, 2NHL, 1HL) “Predicted PM” according to GITMO criteria. The mobilization protocol included G-CSF, administered at a dose of 10μg/kg daily on 4 consecutive days. In the evening of the fourth day, patients received subcutaneous plerixafor at a dose of 0,24 mg/kg. Apheresis was initiated on the fifth day, 10–12 h after plerixafor and 1 h after G-CSF administration. Apheresis and daily administration of G-CSF and plerixafor continued until the patient collected enough CD34+ cells for auto- HSCT (> 2 ×106/kg; max 7 plerixafor injections if required). PBSC collection was initiated if peripheral CD34+ cells count was >10μl. A successful mobilization was defined as a total yeld of > 2×106/kg. RESULTS. 13 patients (76,5%) collected the minimum number of CD34 cells > 2×106/kg. The diagnosis were: 8MM, 1HL,1 NHL. 7 patients (2NHL; 4 MM; 1 LH; 7 predicted) were able to collect > 5×106/Kg. Only 4 patients (3 MM; 1 LNH; 4 proven) failed the mobilization because the numbers of cells CD34 were < 10μL and these patients did not undergo to apheresis procedures. The collection target of 2×106/Kg was reached in a median of 2 apheresis session (range 1–3). The technical characteristics of the procedures were (median value): blood volume processed 12 L (range 9–14), total CD34+/Kg collected 3,06 × 106(range 2,21-8,62), procedure efficiency 47,5% (range 35,3–79), duration of the procedure 261 minutes (range 210–309). Plerixafor was well tolerated and mild side effects were: reactions in the injection site, gastrointestinal disturbs, muscle pain. During administration of plerixafor we did not observe any significant laboratory abnormalities of liver or renal function. CONCLUSION. Unsuccessful mobilization represents an important limitation to ASCT in lymphoma and MM. In our experience plerixafor allowed to collect an appropriate amount of CD34 also in patients defined “proven PM” significantly reducing the percentage of patients that could not undergo ASCT (target value obtained in 43% of “proven PM”). Confirming the recent literature plerixafor is well tolerated with minimal side effects. We retrospectively applied GITMO criteria for PM patients and our experience, although limited, confirm that the use of a correct definition of PM allows the appropriate use of new mobilizing agents like plerixafor increasing significantly the therapeutic options also in patients who had no possibilities to receive an ASCT with the traditional mobilizing therapy. Disclosures: No relevant conflicts of interest to declare.


10.12737/5011 ◽  
2014 ◽  
Vol 21 (2) ◽  
pp. 104-109 ◽  
Author(s):  
Кодяков ◽  
A. Kodyakov ◽  
Груздев ◽  
D. Gruzdev ◽  
Федоров ◽  
...  

This paper is devoted to the actual problem of cosmetology - the procedures of filament rejuvenation of face and neck, which become popular every year. Literature data on the efficacy of these methods are controversial. The authors of most works indicate the minimum number of complications in the practical absence of negative appraisal methodology. The issues of development of the indication for use of some types of filaments and optimal criteria of evaluation of the expected effect in clinical practice are relevant and are discussed in this paper. Taking into account the absence of objective information about long-term consequences, other practical aspects of filament rejuvenation, the authors on the basis of many years of research and experience has specified evaluation criteria and suggested own classification of cosmetic filaments used in the method of filament rejuvenation of face and neck. Installation of filaments with different cosmetic features allows to reaching three different anti-aging effects: lifting, reinforcing and bio-stimulation. The degree of manifestation of these effects depends on the installation method of the thread, but first of all - on the design of conductive filament and needle or cannula. Based on the above data, the authors propose to divide all known cosmetic filaments on the basis of their purpose, proceeding from the achieved effect for three species - lifting, reinforcing and bio-stimulating. The new classification can be used in practice to optimize the selection of filaments for rejuvenation of face and neck and to reduce unintended side effects. The proposed classification of filaments has the purpose of definition of a fundamental criterion for their beauty opportunities. The practical application of this classification contributes to ensure adequate choice of filaments to perform the procedure, reduce side effects and create realistic expectations of doctors and patients from the procedures of the rejuvenation of face and neck.


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