scholarly journals 3d N=4 Bootstrap and Mirror Symmetry

2021 ◽  
Vol 10 (4) ◽  
Author(s):  
Chi-Ming Chang ◽  
Martin Fluder ◽  
Ying-Hsuan Lin ◽  
Shu-Heng Shao ◽  
Yifan Wang

We investigate the non-BPS realm of 3d {N} = 4N=4 superconformal field theory by uniting the non-perturbative methods of the conformal bootstrap and supersymmetric localization, and utilizing special features of 3d {N} = 4N=4 theories such as mirror symmetry and a protected sector described by topological quantum mechanics (TQM). Supersymmetric localization allows for the exact determination of the conformal and flavor central charges, and the latter can be fed into the mini-bootstrap of the TQM to solve for a subset of the OPE data. We examine the implications of the Z_2Z2 mirror action for the SCFT single- and mixed-branch crossing equations for the moment map operators, and apply numerical bootstrap to obtain universal constraints on OPE data for given flavor symmetry groups. A key ingredient in applying the bootstrap analysis is the determination of the mixed-branch superconformal blocks. Among other results, we show that the simplest known self-mirror theory with SU(2) \times SU(2)SU(2)×SU(2) flavor symmetry saturates our bootstrap bounds, which allows us to extract the non-BPS data and examine the self-mirror Z_2Z2 symmetry thereof.

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Aleix Gimenez-Grau ◽  
Pedro Liendo

Abstract We apply the numerical conformal bootstrap to correlators of Coulomb and Higgs branch operators in 4d$$ \mathcal{N} $$ N = 2 superconformal theories. We start by revisiting previous results on single correlators of Coulomb branch operators. In particular, we present improved bounds on OPE coefficients for some selected Argyres-Douglas models, and compare them to recent work where the same cofficients were obtained in the limit of large r charge. There is solid agreement between all the approaches. The improved bounds can be used to extract an approximate spectrum of the Argyres-Douglas models, which can then be used as a guide in order to corner these theories to numerical islands in the space of conformal dimensions. When there is a flavor symmetry present, we complement the analysis by including mixed correlators of Coulomb branch operators and the moment map, a Higgs branch operator which sits in the same multiplet as the flavor current. After calculating the relevant superconformal blocks we apply the numerical machinery to the mixed system. We put general constraints on CFT data appearing in the new channels, with particular emphasis on the simplest Argyres-Douglas model with non-trivial flavor symmetry.


1943 ◽  
Vol 47 (387) ◽  
pp. 103-105
Author(s):  
J. Ratzersdorfer

In cases of tapered struts with hinged or built-in ends where the exact determination of the buckling load is complicated it may be useful to apply a method of successive approximations.Let us first consider a bar of the length l with hinged ends under the action of the compressive force P. The differential equation of the bending line becomeswhere v is the deflection at the section u, v with the moment of inertia I (u) and E is Young's modulus. At the ends of the bar the deflection v is equal to zero (Fig. I).


2017 ◽  
Vol 20 (34) ◽  
pp. 73-84
Author(s):  
Maria Casandra Lucan

Abstract All throughout history the unborn, and implicitly its protection, have been subject for academics and practitioners of various areas. The problem of the origin of the soul and the exact determination of the moment when it is united with the body was crucial in enabling us to define the exact moment when the human life begins, and, consequently, for providing proper protection for the unborn child. In this context visions of the Greek philosophers like Plato, Aristotle, Albertus Magnus and Thomas Aquinas, and of the Latin writer Tertullian, as well as Christian perspectives were analysed in order to identify the starting point of the human being to help determine the level of protection provided for the unborn in history. Finally, considering the fact that not even today has consensus been achieved concerning the beginning of human life, it was and still is difficult to provide proper legal protection for the unborn child, but in our opinion this is by far not impossible.


Author(s):  
Дмитрий Валериевич Судаков ◽  
Олег Валериевич Судаков ◽  
Людмила Валентиновна Кретинина ◽  
Наталья Владимировна Якушева ◽  
Артём Николаевич Шевцов

Статья посвящена построению прогноза эффективности реконструктивных вмешательств на магистральных нервах предплечья в зависимости от протяженности дефекта нервной ткани и особенностей последующего периода реабилитации пациентов. Данная тематика является весьма актуальной, так как с каждым годом во всем мире наблюдается определенный рост случаев травм различного генеза магистральных нервных стволов, которые затем нередко приводят к временной нетрудоспособности и даже инвалидности пациентов. Реконструктивная микрохирургия многие десятилетия пытается решить целый ряд проблем аутотрансплантации нервных стволов и повысить ее общую эффективность. Но из-за определенных проблем связанных с финансированием, некоторые вопросы трансплантологии и реабилитации остаются нерешенными и в настоящий момент. Все это придает представленной работе важное значение не только медицинского, но и социально - экономического плана. Целью работы стала попытка построения прогноза восстановительных операций на нервной ткани, с учетом объема пораженных структур и периода реабилитации. Объектами исследования стало 180 больных, которым по той или иной причине, осуществлялась реконструктивная операция на одном из магистральных нервов предплечья. Все пациенты были разделены на 3 группы по 60 человек, в зависимости от протяженности дефекта магистрального нерва: до 4 см, от 4 до 8 см и от 8 до 12 см. Последующее разделение внутри каждой группы на подгруппы производилось в зависимости от определенного поврежденного нерва (лучевой, локтевой, срединный). В работе изучалось течение раннего послеоперационного воспалительного процесса, с определением бактериальной микрофлоры в ране. Изучались и отдаленные последствия оперативного вмешательства. Своеобразной новизной для данной тематики в целом, стало выявление последующего установления инвалидности пациентов. Кроме того, важные данные были получены и по срокам реабилитации и частичного или полного восстановления утраченных функций по срокам в зависимости от размеров восстанавливаемого дефекта и от наличия или отсутствия необходимой реабилитации. Полученные в работе данные могут представлять интерес не только для врачей хирургов и травматологов, но и для организаторов здравоохранения, позволяя производить прогнозы по выздоровлению пациентов в каждой определенной клинической ситуации The article is devoted to the construction of a forecast of the effectiveness of reconstructive interventions on the main nerves of the forearm, depending on the length of the defect in the nervous tissue and the characteristics of the subsequent period of rehabilitation of patients. This topic is very relevant, since every year all over the world there is a certain increase in cases of injuries of various origins of the main nerve trunks, which then often lead to temporary disability and even disability of patients. For many decades, reconstructive microsurgery has been trying to solve a number of problems of autotransplantation of nerve trunks and improve its overall efficiency. But due to certain problems associated with funding, some issues of transplantation and rehabilitation remain unresolved at the moment. All this gives the presented work important not only medical, but also socio - economic importance. The aim of this work was to attempt to predict restorative operations on the nervous tissue, taking into account the volume of the affected structures and the period of rehabilitation. The objects of the study were 180 patients who, for one reason or another, underwent a reconstructive operation on one of the main nerves of the forearm. All patients were divided into 3 groups of 60 people, depending on the length of the main nerve defect: up to 4 cm, from 4 to 8 cm, and from 8 to 12 cm. Subsequent division within each group into subgroups was performed depending on the specific damaged nerve ( radial, ulnar, median). The work studied the course of the early postoperative inflammatory process, with the determination of bacterial microflora in the wound. The long-term consequences of surgery were also studied. A peculiar novelty for this topic as a whole was the identification of the subsequent establishment of disability in patients. In addition, important data were obtained on the timing of rehabilitation and partial or complete restoration of lost functions in terms of timing, depending on the size of the restored defect and on the presence or absence of the necessary rehabilitation. The data obtained in this work may be of interest not only for surgeons and traumatologists, but also for healthcare organizers, allowing them to make predictions about the recovery of patients in each specific clinical situation


2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yifei He ◽  
Jesper Lykke Jacobsen ◽  
Hubert Saleur

Abstract Based on the spectrum identified in our earlier work [1], we numerically solve the bootstrap to determine four-point correlation functions of the geometrical connectivities in the Q-state Potts model. Crucial in our approach is the existence of “interchiral conformal blocks”, which arise from the degeneracy of fields with conformal weight hr,1, with r ∈ ℕ*, and are related to the underlying presence of the “interchiral algebra” introduced in [2]. We also find evidence for the existence of “renormalized” recursions, replacing those that follow from the degeneracy of the field $$ {\Phi}_{12}^D $$ Φ 12 D in Liouville theory, and obtain the first few such recursions in closed form. This hints at the possibility of the full analytical determination of correlation functions in this model.


1879 ◽  
Vol 29 (196-199) ◽  
pp. 490-493 ◽  

In one former communication “On the Vapour Densities of Potas­sium and Sodium,” we pointed out the chief obstacles which lay in the way of an exact determination of these constants. Having overcome the chief manipulative difficulties in connexion with the method we described, there still remained the problem for solution as to how far the use of iron bottles in our experiments might affect the results. If the iron retained the metals or allowed their vapours to diffuse with rapidity through it, a considerable error might be produced without its being easily detected.


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