scholarly journals Bootstrapping Coulomb and Higgs branch operators

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.

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.


1996 ◽  
Vol 126 (1) ◽  
pp. 65-84 ◽  
Author(s):  
Peter Heinzner ◽  
Alan Huckleberry

Author(s):  
Екатерина Александровна Витоженц ◽  
Александр Викторович Кобелев

Предложен новый способ контроля введения инъекционной иглы в просвет вены на основе измерений электрического импеданса с помощью смешанной системы электродов, состоящей из биполярного и тетраполярного звеньев. Исследованы альтернативные схемы расположения электродов при проведении контроля венозной пункции биоимпедансным методом - они имеют более сложную конструкцию, используют дорогостоящие специализированные коаксиальные иглы, не позволяют однозначно определить факт прокола стенки венозного сосуда, нуждаются в дополнительной фильтрации регистрируемого сигнала с целью корректной интерпретации результата. Эффективность предложенной методики проверялась в ходе экспериментальных исследований на 5 добровольцах. Результаты экспериментов позволили идентифицировать 4 стадии нахождения инъекционной иглы относительно верхней конечности: нет касания, касание кожного покрова, нахождение под кожей коже, попадание в просвет вены. Идентификация положений инъекционной иглы происходит в реальном времени без дополнительной фильтрации регистрируемого сигнала. Метод позволяет обнаружить момент прокола стенки венозного сосуда стандартной инъекционной иглой, что в дальнейшем позволит сэкономить на изготовлении специализированных многослойных игольчатых электродов и внедрить данный способ контроля за проведением венепункции в медицинскую практику. Дальнейшее развитие предложенного подхода предполагает идентификацию двойного прокола вены, дифференцирование типа ткани в процессе введения иглы и исследование возможности определения типа кровеносного сосуда A new method for controlling the penetration of an injection needle into the vein based on measurements of electrical impedance using a mixed system of electrodes consisting of bipolar and tetrapolar parts is proposed. Alternative schemes for the arrangement of electrodes for monitoring venous puncture using the bioimpedance method have been investigated - they have a more complex design, use expensive specialized coaxial needles, do not allow to unambiguously determine the fact of a puncture of the venous vessel wall, require additional filtering of the recorded signal in order to correctly interpret the result. The effectiveness of the proposed technique was tested in experimental studies on 5 volunteers. The results of the experiments made it possible to identify 4 stages of finding the injection needle relative to the upper limb: no touching, touching the skin, being under the skin of the skin, getting into the lumen of the vein. Identification of the positions of the injection needle occurs in real time without additional filtering of the recorded signal. The method allows detecting the moment of puncture of the wall of a venous vessel with a standard injection needle, which in the future will save on the manufacture of specialized multilayer needle electrodes and introduce this method of monitoring venipuncture into medical practice. Further development of the proposed approach involves the identification of a double vein puncture, differentiation of tissue type during needle insertion, and investigation of the possibility of determining the type of blood vessel


2014 ◽  
Vol 14 (1) ◽  
pp. 161-178 ◽  
Author(s):  
Stavroula Tsiplakou
Keyword(s):  

Cypriot and Standard Greek still stand in a diglossic relationship; however, recent work on Cypriot Greek points to ongoing processes of levelling of local sub-varieties and the emergence of a pancypriot koiné. This paper explores patterns of structural mixing between Standard and Cypriot Greek in the Cypriot koiné. The data indicate that structural mixing is mostly achieved through morphological choices, while Cypriot phonology and syntax remain largely intact. The fact that morphology has this capacity of a ‘buffer’ between two presumably competing grammatical systems provides a strong parallel to interlanguage phenomena and a potential account of why the two systems are prevented from merging. Keywords: competing grammars; Cypriot Greek; diglossia; koiné; levelling; Standard Greek


2013 ◽  
Vol 6 (2) ◽  
pp. 85-93
Author(s):  
Anna Ceglarska ◽  

History of the rise of the Roman Republic as described by Polybius The aim of this article is to refer Polybius’s political theory, included in Book VI of The Histories, to the history of the rise of the Roman Republic. This theme must have been particularly significant for Polybius. For him, Rome was the most perfect example of a mixed government system, and the aim of describing its history was to show the development of this perfect system. The article presents the mutual relation of theory and history, starting with the period of kingship, up to the emergence of the democratic element, i.e. the moment when Rome acquired the mixed system of government. Both the political and social contexts of the changes are outlined. The analysis suggests that Polybius related his political theory to the history of the state he admired, thus providing the theory with actual foundations. Reconstructing his analysis makes it possible to see the history of Rome in a different light, and to ponder the system itself and its decline, even though the main objective of both Polybius and this article is to present its development.


10.37236/5038 ◽  
2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Laura Escobar

Bott-Samelson varieties are a twisted product of $\mathbb{C}\mathbb{P}^1$'s with a map into $G/B$. These varieties are mostly studied in the case in which the map into $G/B$ is birational to the image; however in this paper we study a fiber of this map when it is not birational. We prove that in some cases the general fiber, which we christen a brick manifold, is a toric variety. In order to do so we use the moment map of a Bott-Samelson variety to translate this problem into one in terms of the "subword complexes" of Knutson and Miller. Pilaud and Stump realized certain subword complexes as the dual of the boundary of a polytope which generalizes the brick polytope defined by Pilaud and Santos. For a nice family of words, the brick polytope is the generalized associahedron realized by Hohlweg, Lange and Thomas. These stories connect in a nice way: we show that the moment polytope of the brick manifold is the brick polytope. In particular, we give a nice description of the toric variety of the associahedron. We give each brick manifold a stratification dual to the subword complex. In addition, we relate brick manifolds to Brion's resolutions of Richardon varieties.


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