scholarly journals A CLASSICAL N = 4 SUPER W ALGEBRA

1993 ◽  
Vol 08 (20) ◽  
pp. 3615-3630 ◽  
Author(s):  
R. E. C. PERRET
Keyword(s):  
Virasoro Algebra ◽  
Superconformal Algebra ◽  
Ward Identities ◽  
Complete Form

I construct classical superextensions of the Virasoro algebra by employing the Ward identities of a linearly realized subalgebra. For the N = 4 superconformal algebra, this subalgebra is generated by the N = 2 U (1) supercurrent and a spin 0 N = 2 superfield. I show that this structure can be extended to an N = 4 super W3 algebra, and give the complete form of this algebra.

METHOD OF SOLVING CONFORMAL MODELS IN D-DIMENSIONAL SPACE III SECONDARY FIELDS IN D>2 AND THE SOLUTION OF TWO-DIMENSIONAL MODELS

1998 ◽  
Vol 13 (28) ◽  
pp. 4837-4888
Author(s):  
E. S. FRADKIN ◽  
M. YA. PALCHIK
Keyword(s):  
Hilbert Space ◽  
Dimensional Space ◽  
Conformal Symmetry ◽  
Solvable Model ◽  
Virasoro Algebra ◽  
Green Functions ◽  
Two Dimensional ◽  
Ward Identities ◽  
Fundamental Field ◽  
Conformal Models

We proceed with the study (started in Refs. 1 and 2) of the Hilbert space of conformal field theory in D di mensions. We discuss an infinite family of secondary fields [Formula: see text] generated by the action of the components of energy–momentum tensor Tμν on the fundamental (primary) field. It is shown that the states of these fields form a specific sector of the Hilbert space H which is determined by the Ward identities and [Formula: see text]-dimensional conformal symmetry. We demonstrate that for D = 2 the subspace H coincides with the space of representation of the Virasoro algebra. Each exactly solvable model in the case of D ≥ 2 is defined by the requirement of vanishing of a certain state Qs(x)|0> ⊂ H analogous to the null vector of two-dimensional theory. The Green functions of the fields [Formula: see text] are calculated in terms of the Green functions of the fundamental field. It is shown that all the Green functions of the type [Formula: see text] satisfy the anomalous Ward identities. The anomalous contributions are given by the fields [Formula: see text], where s′≤s-1. The fields Qs are constructed as superpositions of secondary fields with the anomalous contribution equal to zero, An approach developed is based on a finite-dimensional conformal symmetry for any D ≥ 2. Nevertheless the resulting models have the structure analogous to that of two-dimensional conformal theories. This analogy is discussed in detail. It is shown that for D = 2 the family of models coincides with the well-known family of conformal models based on infinite-dimensional conformal symmetry. The analysis of this phenomenon indicates the existence of the D-dimensional analog of the Virasoro algebra.

scholarly journals On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions

2020 ◽  
Vol 80 (1) ◽  
Author(s):  
Ricardo Caroca ◽  
Patrick Concha ◽  
Octavio Fierro ◽  
Evelyn Rodríguez
Keyword(s):  
Virasoro Algebra ◽  
Expansion Method ◽  
Superconformal Algebra ◽  
Supersymmetric Extension ◽  
Infinite Dimensional ◽  
Gravity Theories ◽  
Symmetry Generators ◽  
Asymptotic Symmetries ◽  
R Symmetry

AbstractIn this work we obtain known and new supersymmetric extensions of diverse asymptotic symmetries defined in three spacetime dimensions by considering the semigroup expansion method. The super-$$BMS_3$$BMS3, the superconformal algebra and new infinite-dimensional superalgebras are obtained by expanding the super-Virasoro algebra. The new superalgebras obtained are supersymmetric extensions of the asymptotic algebras of the Maxwell and the $$\mathfrak {so}(2,2)\oplus \mathfrak {so}(2,1)$$so(2,2)⊕so(2,1) gravity theories. We extend our results to the $$\mathcal {N}=2$$N=2 and $$\mathcal {N}=4$$N=4 cases and find that R-symmetry generators are required. We also show that the new infinite-dimensional structures are related through a flat limit $$\ell \rightarrow \infty $$ℓ→∞.

A Review of Conformal Field Theory in 2D

2014 ◽  
Vol 6 (2) ◽  
pp. 1079-1105
Author(s):  
Rahul Nigam
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Statistical Mechanics ◽  
Critical Behavior ◽  
Verma Module ◽  
Virasoro Algebra ◽  
Quantum Field ◽  
Conformal Field ◽  
Insight Into

In this review we study the elementary structure of Conformal Field Theory in which is a recipe for further studies of critical behavior of various systems in statistical mechanics and quantum field theory. We briefly review CFT in dimensions which plays a prominent role for example in the well-known duality AdS/CFT in string theory where the CFT lives on the AdS boundary. We also describe the mapping of the theory from the cylinder to a complex plane which will help us gain an insight into the process of radial quantization and radial ordering. Finally we will develop the representation of the Virasoro algebra which is the well-known "Verma module".  

Mesyatseslovs memory of the Russian Orthodox Church

2020 ◽  
pp. 160-198
Author(s):  
Макарий Веретенников
Keyword(s):  
Russian Orthodox ◽  
Orthodox Church ◽  
Russian Orthodox Church ◽  
Analysis And Synthesis ◽  
Liturgical Texts ◽  
History Of ◽  
Complete Form ◽  
Characteristic Features ◽  
Heaven And Earth ◽  
The Church

Статья посвящена содержанию, общим принципам построения и характерным особенностям календаря, или месяцеслова, Русской Православной Церкви. Автор использует методы анализа и синтеза. В итоге делаются нижеследующие обобщения. Месяцеслов был принесён на Русь из Византии в достаточно завершённом виде, однако в процессе исторического развития он дополнился особенными русскими праздниками. Календарь-месяцеслов - это грандиозный собор святых, подвизавшихся в разных местах на протяжении веков, единение Церкви Небесной и земной, история святости и история нашей Церкви. Месяцесловным памятям посвящены составленные гимнографами богослужебные тексты, которые поются и читаются в храмах. Традиционно почитается день кончины угодников Божиих, память открытия мощей святых, перенесения их святых мощей или же день канонизации угодников Божиих, реже - день их рождения. Фенологические наблюдения русского народа связаны с повседневной деятельностью и увязаны с месяцесловом, что свидетельствует о его проникновении в повседневную жизнь русского человека. The article is devoted to the content, General principles of construction and characteristic features of the calendar, or mesyatseslov, of the Russian Orthodox Church. The author uses methods of analysis and synthesis. As a result, the following generalizations are made. The mesyatseslov was brought to Russia from Byzantium in a fairly complete form, but in the course of historical development it was supplemented with special Russian holidays. The calendar-mesyatseslov is a grandiose council of saints who have labored in different places over the centuries, the unity of the Church of Heaven and earth, the history of holiness and the history of our Church. Liturgical texts composed by hymnographers, which are sung and read in churches, are dedicated to the mesyatseslovs memory. Traditionally, the day of the death of saints, the memory of the discovery of the relics of saints, the transfer of their Holy relics, or the day of the canonization of saints, less often - the day of their birth are honored. Russian people’s phenological observations are related to their daily activities and are linked to mesyatseslov, which indicates its penetration into the daily life of the Russian people.

scholarly journals A Complete CDW Theory for the Single Ionization of Multielectronic Atoms by Bare Ion Impact

Atoms ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 3
Author(s):  
Juan M. Monti ◽  
Michele A. Quinto ◽  
Roberto D. Rivarola
Keyword(s):  
Transition Amplitude ◽  
Emission Spectra ◽  
Heavy Ion ◽  
Distorted Wave ◽  
Single Ionization ◽  
Complete Form ◽  
Active Electron ◽  
Ion Impact ◽  
Range Part ◽  
The Continuum

A complete form of the post version of the continuum distorted wave (CDW) theory is used to investigate the single ionization of multielectronic atoms by fast bare heavy ion beams. The influence of the non-ionized electrons on the dynamic evolution is included through a residual target potential considered as a non-Coulomb central potential through a GSZ parametric one. Divergences found in the transition amplitude containing the short-range part of the target potential are avoided by considering, in that term exclusively, an eikonal phase instead of the continuum factor as the initial channel distortion function. In this way, we achieve the inclusion of the interaction between the target active electron and the residual target, giving place to a more complete theory. The present analysis is supported by comparisons with existing experimental electron emission spectra and other distorted wave theories.

scholarly journals On local and integrated stress-tensor commutators

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Mert Besken ◽  
Jan de Boer ◽  
Grégoire Mathys
Keyword(s):  
Stress Tensor ◽  
Free Field ◽  
Virasoro Algebra ◽  
Light Sheet ◽  
Operator Product ◽  
Local Form ◽  
Two Dimensional ◽  
Conformal Embedding ◽  
General Aspects ◽  
The Right

Abstract We discuss some general aspects of commutators of local operators in Lorentzian CFTs, which can be obtained from a suitable analytic continuation of the Euclidean operator product expansion (OPE). Commutators only make sense as distributions, and care has to be taken to extract the right distribution from the OPE. We provide explicit computations in two and four-dimensional CFTs, focusing mainly on commutators of components of the stress-tensor. We rederive several familiar results, such as the canonical commutation relations of free field theory, the local form of the Poincaré algebra, and the Virasoro algebra of two-dimensional CFT. We then consider commutators of light-ray operators built from the stress-tensor. Using simplifying features of the light sheet limit in four-dimensional CFT we provide a direct computation of the BMS algebra formed by a specific set of light-ray operators in theories with no light scalar conformal primaries. In four-dimensional CFT we define a new infinite set of light-ray operators constructed from the stress-tensor, which all have well-defined matrix elements. These are a direct generalization of the two-dimensional Virasoro light-ray operators that are obtained from a conformal embedding of Minkowski space in the Lorentzian cylinder. They obey Hermiticity conditions similar to their two-dimensional analogues, and also share the property that a semi-infinite subset annihilates the vacuum.

scholarly journals Ward identities in dual string theories

1986 ◽  
Vol 167 (4) ◽  
pp. 388-392 ◽  
Author(s):  
G. Veneziano
Keyword(s):  
Ward Identities ◽  
String Theories
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