scholarly journals STRESS–TENSOR FOR PARAFERMIONS FROM WINDING SUBALGEBRAS OF AFFINE ALGEBRAS

1998 ◽  
Vol 13 (11) ◽  
pp. 853-860 ◽  
Author(s):  
VINCENZO MAROTTA
Keyword(s):  
Stress Tensor ◽  
Free Field ◽  
Virasoro Algebra ◽  
Standard Level ◽  
Affine Algebras ◽  
Background Charge

We discuss a realization of stress–tensor for parafermion theories following a construction for higher level affine algebras, based on the projection of the standard level-one bosonic realization on the winding subalgebra. All the fields are obtained from rank free bosons compactified on torus, d. This gives an alternative realization of Virasoro algebra in terms of a nonlocal correction of a free field construction which does not fit the usual background charge of the Feigin–Fuchs approach.

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 A NOTE ON KERR/CFT AND FREE FIELDS

2010 ◽  
Vol 25 (20) ◽  
pp. 3965-3973 ◽  
Author(s):  
JØRGEN RASMUSSEN
Keyword(s):  
Black Hole ◽  
Boundary Conditions ◽  
Isometry Group ◽  
Free Field ◽  
Kerr Black Hole ◽  
Virasoro Algebra ◽  
Free Fields ◽  
Horizon Geometry

The near-horizon geometry of the extremal four-dimensional Kerr black hole and certain generalizations thereof has an SL (2, ℝ) × U (1) isometry group. Excitations around this geometry can be controlled by imposing appropriate boundary conditions. For certain boundary conditions, the U(1) isometry is enhanced to a Virasoro algebra. Here, we propose a free-field construction of this Virasoro algebra.

scholarly journals The N = 1 super Heisenberg–Virasoro vertex algebra at level zero

2021 ◽  
Author(s):  
Dražen Adamović ◽  
Berislav Jandrić ◽  
Gordan Radobolja
Keyword(s):  
Fock Space ◽  
Free Field ◽  
Virasoro Algebra ◽  
Vertex Algebra ◽  
Verma Modules ◽  
Minimal Models ◽  
Highest Weight ◽  
Level Zero ◽  
Free Field Realization ◽  
Highest Weight Representations

We study the representation theory of the [Formula: see text] super Heisenberg–Virasoro vertex algebra at level zero, which extends the previous work on the Heisenberg–Virasoro vertex algebra [D. Adamović and G. Radobolja, Free field realization of the twisted Heisenberg–Virasoro algebra at level zero and its applications, J. Pure Appl. Algebra 219(10) (2015) 4322–4342; D. Adamović and G. Radobolja, Self-dual and logarithmic representations of the twisted Heisenberg–Virasoro algebra at level zero, Commun. Contemp. Math. 21(2) (2019) 1850008; Y. Billig, Representations of the twisted Heisenberg–Virasoro algebra at level zero, Can. Math. Bull. 46(4) (2003) 529–537] to the super case. We calculated all characters of irreducible highest weight representations by investigating certain Fock space representations. Quite surprisingly, we found that the maximal submodules of certain Verma modules are generated by subsingular vectors. The formulas for singular and subsingular vectors are obtained using screening operators appearing in a study of certain logarithmic vertex algebras [D. Adamović and A. Milas, On W-algebras associated to [Formula: see text] minimal models and their representations, Int. Math. Res. Notices 2010(20) (2010) 3896–3934].

scholarly journals Representations for three-point Lie algebras of genus zero

2019 ◽  
Vol 30 (14) ◽  
pp. 1950070
Author(s):  
Dong Liu ◽  
Yufeng Pei ◽  
Limeng Xia
Keyword(s):  
Lie Algebras ◽  
Virasoro Algebra ◽  
Vertex Operators ◽  
Affine Algebra ◽  
Genus Zero ◽  
Simple Modules ◽  
Affine Algebras

In this paper, we study representations for three-point Lie algebras of genus zero based on the Cox–Jurisich’s presentations. We construct two functors which transform simple restricted modules with nonzero levels over the standard affine algebras into simple modules over the three-point affine algebras of genus zero. As a corollary, vertex representations are constructed for the three-point affine algebra of genus zero using vertex operators. Moreover, we construct a Fock module for certain quotient of three-point Virasoro algebra of genus zero.

CLASSICAL EXTENDED SUPERCONFORMAL SYMMETRIES

1992 ◽  
Vol 07 (19) ◽  
pp. 4501-4519 ◽  
Author(s):  
R. RAJU VISWANATHAN
Keyword(s):  
Stress Tensor ◽  
Differential Operators ◽  
Free Field ◽  
Two Dimensions ◽  
Superconformal Algebra ◽  
Field Representation ◽  
Closed Algebra ◽  
Super Symmetry

Supercovariant differential operators are defined in two dimensions which map super-symmetry doublets to other doublets. The possibility of constructing a closed algebra among the fields appearing in such operators is explored. Such an algebra exists for Grassmann-odd differential operators. A representation for these operators in terms of free field doublets is constructed. An explicit closed algebra involving fields of spin 2 and 5/2, in addition to the stress tensor and the supersymmetry generator, is constructed from such a free field representation as an example of a nonlinear extended superconformal algebra.

scholarly journals FREE FIELD CONSTRUCTIONS FOR THE ELLIPTIC ALGEBRA $\rscr{A}_{q,p}(\widehat{sl}_2)$ AND BAXTER'S EIGHT-VERTEX MODEL

2004 ◽  
Vol 19 (supp02) ◽  
pp. 363-380 ◽  
Author(s):  
J. SHIRAISHI
Keyword(s):  
Integral Formula ◽  
Free Field ◽  
Virasoro Algebra ◽  
Vertex Operators ◽  
Vertex Model ◽  
Elliptic Algebra ◽  
Deformed Virasoro Algebra ◽  
The One ◽  
Level 2 ◽  
Elliptic Quantum

Three examples of free field constructions for the vertex operators of the elliptic quantum group [Formula: see text] are obtained. Two of these ( for p1/2=±q3/2, p1/2=-q2) are based on representation theories of the deformed Virasoro algebra, which correspond to the level 4 and level 2 Z-algebra of Lepowsky and Wilson. The third one (p1/2=q3) is constructed over a tensor product of a bosonic and a fermionic Fock spaces. The algebraic structure at (p1/2=q3), however, is not related to the deformed Virasoro algebra. Using these free field constructions, an integral formula for the correlation functions of Baxter's eight-vertex model is obtained. This formula shows different structure compared with the one obtained by Lashkevich and Pugai.

scholarly journals BEYOND THE LARGE N LIMIT: NON-LINEAR W∞ AS SYMMETRY OF THE SL(2,R)/U(1) COSET MODEL

1992 ◽  
Vol 07 (supp01a) ◽  
pp. 55-81 ◽  
Author(s):  
IOANNIS BAKAS ◽  
ELIAS KIRITSIS
Keyword(s):  
Black Hole ◽  
String Theory ◽  
Free Field ◽  
Symmetry Algebra ◽  
Linear Deformation ◽  
Coset Model ◽  
Large N ◽  
Free Field Realization ◽  
Non Linear ◽  
Background Charge

We show that the symmetry algebra of the SL(2,R)k/ U(1) coset model is a non-linear deformation of W∞, characterized by k. This is a universal W-algebra which linearizes in the large k limit and truncates to WN for K=-N. Using the theory of non-compact parafermions we construct a free field realization of the non-linear W∞ in terms of two bosons with background charge. The W-characters of all unitary SL(2,R)/ U(1) representations are computed. Applications to the physics of 2-d black hole backgrounds are also discussed and connections with the KP approach to c=1 string theory are outlined.

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