Two-dimensional conformal quantum field theory

Furlan, P.; Sotkov, G. M.; Todorov, Ivan

doi:10.1007/bf02742979

Cited by 61 publications

(105 citation statements)

References 201 publications

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“…This equation is obtained by applying the current algebra and the normal ordering prescription for currents [FST89]. The matrix C α 2 stands for the second Casimir element of h α in the representation Ad g • ι| hα , if h α is a simple ideal.…”

Section: Characterisation Of Conformal Inclusionsmentioning

confidence: 99%

“…First, one may restrict attention to colours T c ∈ ι(h) ⊥ since the weighted Casimir respects the orthogonal decomposition g = ι(h) + ι(h) ⊥ with respect to Ad • ι and Θ g − Θ h commutes with all currents whose colours are in ι(h). "All" that one has to do is to apply the general commutation relation (1) restricted to colours from ι(h) ⊥ , follow carefully the normal ordering of currents, observe symmetries of group theoretical coefficients, keep in mind T c ∈ ι(h) ⊥ , calculate some n-point functions of currents following the scheme in [FST89], use Jacobi's identity a few times and recognise the second Casimir element in the adjoint representation, which amounts to twice the dual Coxeter number. With all that, it is a straightforward algebraic exercise.…”

Section: Covariant and Invariant Coloursmentioning

confidence: 99%

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Conformal Covariance Subalgebras

Köster

2004

Letters in Mathematical Physics

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We give a direct Lie algebraic characterisation of conformal inclusions of chiral current algebras associated with compact, reductive Lie algebras. We use quantum field theoretic arguments and prove a longstanding conjecture of Schellekens and Warner on grounds of unitarity and positivity of energy. We explore the structures found to characterise conformal covariance subalgebras and coset current algebras.

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Section: Characterisation Of Conformal Inclusionsmentioning

confidence: 99%

Section: Covariant and Invariant Coloursmentioning

confidence: 99%

Conformal Covariance Subalgebras

Köster

2004

Letters in Mathematical Physics

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“…At this point we are going to follow closely the method described in detail in section (3.5) of ref. [8]. As a result of a simple and standard computation we obtain the following OPE's algebra:…”

Section: Introductionmentioning

confidence: 99%

Off-Critical Current Algebras

Abdalla

Sotkov

et al. 1995

Int. J. Mod. Phys. A

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We discuss the infinite dimensional algebras appearing in integrable perturbations of conformally invariant theories, with special emphasis in the structure of the consequent non-abelian infinite dimensional algebra generalizing W ∞ to the case of a non abelian group. We prove that the pure left-symmetry as well as the pure right-sector of the thus obtained algebra coincides with the conformally invariant case. The mixed sector is more involved, although the general structure seems to be near to be unraveled. We also find some subalgebras that correspond to Kac-Moody algebras. The constraints imposed by the algebras are very strong, and in the case of the massive deformation of a non-abelian fermionic model, the symmetry alone is enough to fix the 2-and 3-point functions of the theory. Universidade de São Paulo

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“…There are several books and review articles [23][24][25] on d = 1 + 1 conformal as well as on massive factorizing models [17,18]. To the extend that concepts and mathematical structures are used which permit no known generalization to higher dimensions (e.g., KacMoody algebras, loop groups, integrability, presence of an infinite number of conservation laws), their line of approach will not be followed in this report since our primary interest will be the use of two-dimensional models of QFT as ''theoretical laboratories'' of general QFT as stated in the abstract.…”

Section: Early History Of Two-dimensional Solved Models and The Problmentioning

confidence: 99%

Two-dimensional models as testing ground for principles and concepts of local quantum physics

Schroer

2006

Annals of Physics

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In the past two-dimensional models of QFT have served as theoretical laboratories for testing new concepts under mathematically controllable condition. In more recent times low-dimensional models (e.g., chiral models, factorizing models) often have been treated by special recipes in a way which sometimes led to a loss of unity of QFT. In the present work, I try to counteract this apartheid tendency by reviewing past results within the setting of the general principles of QFT. To this I add two new ideas: (1) a modular interpretation of the chiral model Diff(S)-covariance with a close connection to the recently formulated local covariance principle for QFT in curved spacetime and (2) a derivation of the chiral model temperature duality from a suitable operator formulation of the angular Wick rotation (in analogy to the Nelson-Symanzik duality in the Ostertwalder-Schrader setting) for rational chiral theories. The SL (2, Z) modular Verlinde relation is a special case of this thermal duality and (within the family of rational models) the matrix S appearing in the thermal duality relation becomes identified with the statistics character matrix S. The relevant angular ''Euclideanization'' is done in the setting of the Tomita-Takesaki modular formalism of operator algebras. I find it appropriate to dedicate this work to the memory of J.A. Swieca with whom I shared the interest in two-dimensional models as a testing ground for QFT for more than one decade. This is a significantly extended version of an ''Encyclopedia of Mathematical Physics'' contribution hep-th/0502125.

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Two-dimensional conformal quantum field theory

Cited by 61 publications

References 201 publications

Conformal Covariance Subalgebras

Conformal Covariance Subalgebras

Off-Critical Current Algebras

Two-dimensional models as testing ground for principles and concepts of local quantum physics

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