scholarly journals Coinvariants of nilpotent subalgebras of the Virasoro algebra and partition identities

1993 ◽  
pp. 139-148 ◽  
Author(s):  
B. Feigin ◽  
E. Frenkel
Keyword(s):  
Virasoro Algebra ◽  
Partition Identities ◽  
Nilpotent Subalgebras

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".  

scholarly journals Proofs of some partition identities conjectured by Kanade and Russell

2021 ◽  
Author(s):  
Hjalmar Rosengren
Keyword(s):  
Lie Algebra ◽  
Partition Identities ◽  
Partition Identity ◽  
Affine Lie Algebra ◽  
Level 2

AbstractKanade and Russell conjectured several Rogers–Ramanujan-type partition identities, some of which are related to level 2 characters of the affine Lie algebra $$A_9^{(2)}$$ A 9 ( 2 ) . Many of these conjectures have been proved by Bringmann, Jennings-Shaffer and Mahlburg. We give new proofs of five conjectures first proved by those authors, as well as four others that have been open until now. Our proofs for the new cases use quadratic transformations for Askey–Wilson and Rogers polynomials. We also obtain some related results, including a partition identity conjectured by Capparelli and first proved by Andrews.

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.

On Lie Algebras with Many Nilpotent Subalgebras

2006 ◽  
Vol 34 (2) ◽  
pp. 595-600 ◽  
Author(s):  
Alexander A. Lashkhi ◽  
Irene Zimmermann
Keyword(s):  
Lie Algebras ◽  
Nilpotent Subalgebras

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.

Automorphisms and Verma Modules for Generalized 2-dim Affine-Virasoro Algebra

2017 ◽  
Vol 24 (02) ◽  
pp. 285-296 ◽  
Author(s):  
Wenlan Ruan ◽  
Honglian Zhang ◽  
Jiancai Sun
Keyword(s):  
Automorphism Group ◽  
Verma Module ◽  
Virasoro Algebra ◽  
Verma Modules

We study the structure of the generalized 2-dim affine-Virasoro algebra, and describe its automorphism group. Furthermore, we also determine the irreducibility of a Verma module over the generalized 2-dim affine-Virasoro algebra.

scholarly journals New proof to Somos’s Dedekind eta-function identities of level 10

2021 ◽  
Author(s):  
B. R. Srivatsa Kumar ◽  
Shruthi
Keyword(s):  
Dedekind Eta Function ◽  
Partition Identities

AbstractMichael Somos used PARI/GP script to generate several Dedekind eta-function identities by using computer. In the present work, we prove two new Dedekind eta-function identities of level 10 discovered by Somos in two different methods. Also during this process, we give an alternate method to Somos’s Dedekind eta-function identities of level 10 proved by B. R. Srivatsa Kumar and D. Anu Radha. As an application of this, we establish colored partition identities.

scholarly journals A FOUR-DIMENSIONAL SUPERSTRING FROM THE BOSONIC STRING WITH SOME APPLICATIONS

2005 ◽  
Vol 20 (01) ◽  
pp. 99-128 ◽  
Author(s):  
B. B. DEO ◽  
L. MAHARANA
Keyword(s):  
Standard Model ◽  
Central Charge ◽  
Virasoro Algebra ◽  
Low Energy ◽  
Majorana Fermions ◽  
Modular Invariance ◽  
Model Group ◽  
Supersymmetry Algebra ◽  
Four Dimensions ◽  
Bosonic Representation

A string in four dimensions is constructed by supplementing it with 44 Majorana fermions. The later are represented by 11 vectors in the bosonic representation SO (D-1,1). The central charge is 26. The fermions are grouped in such a way that the resulting action is worldsheet supersymmetric. The energy–momentum and current generators satisfy the super-Virasoro algebra. GSO projections are necessary for proving modular invariance. Space–time supersymmetry algebra is deduced and is substantiated for specific modes of zero mass. The symmetry group of the model can descend to the low energy standard model group SU (3)× SU L(2)× U Y(1) through the Pati–Salam group.

Sign in / Sign up

Export Citation Format

Share Document