Free-field resolutions of unitary representations of theN=2 virasoro algebra: II. The butterfly resolution

1999 ◽  
Vol 121 (2) ◽  
pp. 1462-1472 ◽  
Author(s):  
A. M. Semikhatov ◽  
B. L. Feigin
Keyword(s):  
Free Field ◽  
Virasoro Algebra ◽  
Unitary Representations ◽  
Algebra Ii

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 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.

Unitary representations of the Virasoro algebra

1986 ◽  
Vol 53 (4) ◽  
pp. 1013-1046 ◽  
Author(s):  
Akihiro Tsuchiya ◽  
Yukihiro Kanie
Keyword(s):  
Virasoro Algebra ◽  
Unitary Representations

scholarly journals UNITARY REPRESENTATIONS OF W INFINITY ALGEBRAS

1992 ◽  
Vol 07 (25) ◽  
pp. 6339-6355 ◽  
Author(s):  
SATORU ODAKE
Keyword(s):  
Central Charge ◽  
Discrete Series ◽  
Free Field ◽  
Unitary Representations ◽  
Continuous Series ◽  
Highest Weight ◽  
Free Field Realization ◽  
Highest Weight Representations

We study the irreducible unitary highest weight representations, which are obtained from free field realizations, of W infinity algebras [Formula: see text] with central charges (2, 1, 3, 2M, N, 2M+N). The characters of these representations are computed. We construct a new extended superalgebra [Formula: see text], whose bosonic sector is [Formula: see text]. Its representations obtained from a free field realization with central charge 2M+N, are classified into two classes: continuous series and discrete series. For the former there exists a supersymmetry, but for the latter a supersymmetry exists only for M=N.

scholarly journals UNITARY REPRESENTATIONS FOR THE SCHRÖDINGER–VIRASORO LIE ALGEBRA

2012 ◽  
Vol 12 (01) ◽  
pp. 1250132 ◽  
Author(s):  
XIUFU ZHANG ◽  
SHAOBIN TAN
Keyword(s):  
Lie Algebra ◽  
Virasoro Algebra ◽  
Unitary Representations

In this paper, conjugate-linear anti-involutions and unitary Harish-Chandra modules over the Schrödinger–Virasoro algebra are studied. It is proved that there are only two classes conjugate-linear anti-involutions over the Schrödinger–Virasoro algebra. The main result of this paper is that a unitary Harish-Chandra module over the Schrödinger–Virasoro algebra is simply a unitary Harish-Chandra module over the Virasoro algebra.

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.

Sign in / Sign up

Export Citation Format

Share Document