Toward classification of conformal theories
TL;DR: In this paper, the authors studied the representations of the mapping class groups which arise in 2D conformal theories and derived some restrictions on the value of the conformal dimension hi of operators and the central charge c of the Virasoro algebra.
About: This article is published in Physics Letters B.The article was published on 1988-05-26. It has received 166 citations till now. The article focuses on the topics: Primary field & Conformal field theory.
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TL;DR: In this article, a spin-1/2 system on a honeycomb lattice is studied, where the interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength.
4,032 citations
TL;DR: In this article, the authors define the classical limit of a conformal field theory as a limit in which the conformal weights of all primary fields vanish, and define chiral vertex operators and duality matrices and review the fundamental identities they satisfy.
Abstract: We define chiral vertex operators and duality matrices and review the fundamental identities they satisfy. In order to understand the meaning of these equations, and therefore of conformal field theory, we define the classical limit of a conformal field theory as a limit in which the conformal weights of all primary fields vanish. The classical limit of the equations for the duality matrices in rational field theory together with some results of category theory, suggest that (quantum) conformal field theory should be regarded as a generalization of group theory.
1,305 citations
Cites background or methods from "Toward classification of conformal ..."
...This relation was noticed in [30] and was used in [30] and [10]...
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...It seems that imposing a finiteness condition, defining what are known as rational conformal field theories, offers the best prospects for further progress [1-19]....
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TL;DR: In this paper, the chiral properties of (orbifold) conformal field theories were analyzed by modding out by a finite symmetry group, and the fusion rules were derived by studying the modular transformation properties of one-loop characters.
Abstract: We analyze the chiral properties of (orbifold) conformal field theories which are obtained from a given conformal field theory by modding out by a finite symmetry group. For a class of orbifolds, we derive the fusion rules by studying the modular transformation properties of the one-loop characters. The results are illustrated with explicit calculations of toroidal andc=1 models.
603 citations
TL;DR: In this paper, the duality matrices satisfy a finite number of independent polynomial equations, which imply constraints on monodromies allowed in rational conformal field theories.
503 citations
TL;DR: In this paper, a new notion of the core of a braided fusion category is introduced, which allows to separate the part of a fusion category that does not come from finite groups.
Abstract: We introduce a new notion of the core of a braided fusion category. It allows to separate the part of a braided fusion category that does not come from finite groups. We also give a comprehensive and self-contained exposition of the known results on braided fusion categories without assuming them pre-modular or non-degenerate. The guiding heuristic principle of our work is an analogy between braided fusion categories and Casimir Lie algebras.
384 citations
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TL;DR: In this paper, the authors present an investigation of the massless, two-dimentional, interacting field theories and their invariance under an infinite-dimensional group of conformal transformations.
4,595 citations
TL;DR: In this paper, it was shown how conformal invariance relates many numerically accessible properties of the transfer matrix of a critical system in a finite-width infinitely long strip to bulk universal quantities.
1,951 citations
TL;DR: In this article, the authors show that conformal invariance and unitarity severely limit the possible values of critical exponents in two-dimensional systems, and propose a solution to this problem.
Abstract: Conformal invariance and unitarity severely limit the possible values of critical exponents in two-dimensional systems.
1,034 citations
TL;DR: A1(1) Kac-Moody algebras have been studied in this paper for modular invariant sesquilinear theories with positive integral coefficients.
Abstract: We present a detailed and complete proof of our earlier conjecture on the classification of minimal conformal invariant theories. This is based on an exhaustive construction of all modular invariant sesquilinear forms, with positive integral coefficients, in the characters of the Virasoro or of theA1(1) Kac-Moody algebras, which describe the corresponding partition functions on a torus. A remarkable correspondence emerges with simply laced Lie algebras.
556 citations
TL;DR: In this paper, a systematic study of modular invariance of partition functions is presented, relevant both for two-dimensional minimal conformal invariant theories and for string propagation on a SU(2) group manifold.
535 citations