Operator Algebras and Conformal Field Theory

1995 ◽  
pp. 966-979 ◽  
Author(s):  
Antony J. Wassermann
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Operator Algebras ◽  
Conformal Field

scholarly journals Operator algebras and conformal field theory

1993 ◽  
Vol 155 (3) ◽  
pp. 569-640 ◽  
Author(s):  
Fabrizio Gabbiani ◽  
Jürg Fröhlich
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Operator Algebras ◽  
Conformal Field

scholarly journals Correlator correspondences for subregular $$ \mathcal{W} $$-algebras and principal $$ \mathcal{W} $$-superalgebras

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Thomas Creutzig ◽  
Yasuaki Hikida ◽  
Devon Stockal
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Path Integral ◽  
Vertex Operator ◽  
Operator Algebras ◽  
Natural Generalization ◽  
Weak Duality ◽  
Two Dimensional ◽  
Conformal Field ◽  
Corner Vertex

Abstract We examine a strong/weak duality between a Heisenberg coset of a theory with $$ \mathfrak{sl} $$ sl n subregular $$ \mathcal{W} $$ W -algebra symmetry and a theory with a $$ \mathfrak{sl} $$ sl n|1-structure. In a previous work, two of the current authors provided a path integral derivation of correlator correspondences for a series of generalized Fateev-Zamolodchikov-Zamolodchikov (FZZ-)duality. In this paper, we derive correlator correspondences in a similar way but for a different series of generalized duality. This work is a part of the project to realize the duality of corner vertex operator algebras proposed by Gaiotto and Rapčák and partly proven by Linshaw and one of us in terms of two dimensional conformal field theory. We also examine another type of duality involving an additional pair of fermions, which is a natural generalization of the fermionic FZZ-duality. The generalization should be important since a principal $$ \mathcal{W} $$ W -superalgebra appears as its symmetry and the properties of the superalgebra are less understood than bosonic counterparts.

Operator algebras and conformal field theory

1998 ◽  
Vol 133 (3) ◽  
pp. 467-538 ◽  
Author(s):  
Antony Wassermann
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Operator Algebras ◽  
Conformal Field

scholarly journals THE NICHOLS ALGEBRA OF SCREENINGS

2012 ◽  
Vol 14 (04) ◽  
pp. 1250029 ◽  
Author(s):  
A. M. SEMIKHATOV ◽  
I. YU. TIPUNIN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Operator Algebras ◽  
Local System ◽  
The Other ◽  
Vertex Operators ◽  
Two Dimensional ◽  
Nichols Algebra ◽  
Conformal Field ◽  
Algebraic Counterpart

Two related constructions are associated with screening operators in models of two-dimensional conformal field theory. One is a local system constructed in terms of the braided vector space X spanned by the screening species in a given CFT model and the space of vertex operators Y and the other is the Nichols algebra 𝔅(X) and the category of its Yetter–Drinfeld modules, which we propose as an algebraic counterpart, in a "braided" version of the Kazhdan–Lusztig duality, of the representation category of vertex-operator algebras realized in logarithmic CFT models.

scholarly journals Lorentzian dynamics and factorization beyond rationality

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Chi-Ming Chang ◽  
Ying-Hsuan Lin
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Operator Algebras ◽  
Topological Defect ◽  
Conformal Field ◽  
Defect Operator ◽  
Bulk Scattering ◽  
Boson Theory ◽  
Local Operators ◽  
Twist Fields

Abstract We investigate the emergence of topological defect lines in the conformal Regge limit of two-dimensional conformal field theory. We explain how a local operator can be factorized into a holomorphic and an anti-holomorphic defect operator connected through a topological defect line, and discuss implications on analyticity and Lorentzian dynamics including aspects of chaos. We derive a formula relating the infinite boost limit, which holographically encodes the “opacity” of bulk scattering, to the action of topological defect lines on local operators. Leveraging the unitary bound on the opacity and the positivity of fusion coefficients, we show that the spectral radii of a large class of topological defect lines are given by their loop expectation values. Factorization also gives a formula relating the local and defect operator algebras and fusion categorical data. We then review factorization in rational conformal field theory from a defect perspective, and examine irrational theories. On the orbifold branch of the c = 1 free boson theory, we find a unified description for the topological defect lines through which the twist fields are factorized; at irrational points, the twist fields factorize through “non-compact” topological defect lines which exhibit continuous defect operator spectra. Along the way, we initiate the development of a formalism to characterize non-compact topological defect lines.

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