A new n = 6 superconformal algebra
TL;DR: In this paper, a new N = 6 superconformal algebra which extends the Virasoro algebra by the SO 6 current algebra, by 6 odd primary fields of conformal weight 3/2 and by 10 odd primary field of conformally weight 1/2, is presented.
Abstract: In this paper we construct a newN = 6 superconformal algebra which extends the Virasoro algebra by theSO
6 current algebra, by 6 odd primary fields of conformal weight 3/2 and by 10 odd primary fields of conformal weight 1/2. The commutation relations of this algebra, which we will refer to asCK
6, are represented by short distance operator product expansions (OPE). We constructCK
6, as a subalgebra of theSO(6) superconformal algebra K6, thus giving it a natural representation as first order differential operators on the circle withN = 6 extended symmetry. We show thatCK
6 has no nontrivial central extensions.
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TL;DR: In this paper, the memory of my friend Boris Weisfeiler is dedicated to his work in mathematics, a remarkable man and mathematician, who was a pioneer in many fields.
176 citations
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TL;DR: Conformal algebra is an axiomatic description of the operator product expansion (or rather its Fourier transform) of chiral fields in a conformal field theory.
Abstract: Conformal algebra is an axiomatic description of the operator product expansion (or rather its Fourier transform) of chiral fields in a conformal field theory. This is a review of recent developments in the subject.
124 citations
TL;DR: In this paper, the authors classified "quadratic" conformal superalgebras by certain compatible pairs of a Lie superalgebra and a Novikov super-algebra.
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TL;DR: In this paper, simple complex Lie superalgebras of vector fields on "supercircles" are defined and described, and three nontrivial cocycles on the N=4 extended Neveu-Schwarz and Ramond superalgebra are presented.
Abstract: We define and describe simple complex Lie superalgbras of vector fields on "supercircles" - simple stringy superalgebras. There are four series of such algebras and four exceptional stringy superalgebras. The 13 of the simple stringy Lie superalgebras are distinguished: only they have nontrivial central extensions; since two of the distinguish algebras have 3 nontrivial central extensions each, there are exactly 16 superizations of the Liouville action, Schroedinger equation, KdV hierarchy, etc. We also present the three nontrivial cocycles on the N=4 extended Neveu-Schwarz and Ramond superalgebras in terms of primary fields and describe the "classical" stringy superalgebras close to the simple ones. One of these stringy superalgebras is a Kac-Moody superalgebra G(A) with a nonsymmetrizable Cartan matrix A. Unlike the Kac-Moody superalgebras of polynomial growth with symmetrizable Cartan matrix, it can not be interpreted as a central extension of a twisted loop algebra.The stringy superalgebras are often referred to as superconformal ones. We discuss how superconformal stringy superalgebras really are.
109 citations
Cites methods from "A new n = 6 superconformal algebra"
...is numerous letters to I. Shchepochkina in October-November 1996 encouraged us to struggle with the crashing computer systems and TEX. While the TEX-file was beeing processed, we got a recent preprint [CK] by Cheng Shun-Jen and V. Kac, where our example kasL is described in different terms. We thank Kac for the kind letter (sent to Leites) that aknowledges his receiving of a preprint of [Sch] and intere...
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TL;DR: In this paper, the authors classify ''quadratic'' conformal superalgebras by certain compatible pairs of a Lie superalgebra and a Novikov super algebra.
Abstract: In this paper, we shall classify ``quadratic'' conformal superalgebras by certain compatible pairs of a Lie superalgebra and a Novikov superalgebra.Four general constructions of such pairs are given. Moreover, we shall classify such pairs related to simple Novikov algebras.
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01 Jan 1997TL;DR: In this paper, a formal distribution a(z,w) = 2 QFT and chiral algebras is defined and the Virasoro algebra is defined, which is a generalization of the Wightman axioms.
Abstract: Preface. 1: Wightman axioms and vertex algebras. 1.1: Wightman axioms of a QFT. 1.2: d = 2 QFT and chiral algebras. 1.3: Definition of a vertex algebra. 1.4: Holomorphic vertex algebras. 2: Calculus of formal distributions. 2.1: Formal delta-function. 2.2: An expansion of a formal distribution a(z,w). 2.3: Locality. 2.4: Taylor's formula. 2.5: Current algebras. 2.6: Conformal weight and the Virasoro algebra. 2.7: Lie superalgebras of formal distributions and conformal superalgebras. 3: Local fields. 3.1: Normally ordered product. 3.2: Dong's lemma. 3.3: Wick's theorem and a "non-commutative" generalization. 3.4: Restricted and field representations of Lie superalgebras of formal distributions. 3.5: Free (super)bosoms. 3.5: Free (super)fermions. 4: Structure theory of vertex algebras. 4.1: Consequences of translation covariance. 4.2: Quasisymmetry. 4.3: Superalgebras, ideals, and tensor products. 4.4: Uniqueness theorem. 4.5: Existence theorem. 4.6: Borcherds OPE formula. 4.7: Vertex algebras associated to Lie superalgebras of formal distributions. 4.8: Borcherds identity. 4.9: Graded and Mobius conformal vertex algebras. 4.10: Conformal vertex algebras. 4.11: Field algebras. 5: Examples of vertex algebras and their applications. 5.1: Charged free fermions. 5.2: Boson-fermion correspondence and KP hierarchy. 5.3: gl and W. 5.4: Lattice vertex algebras. 5.5: Simple lattice vertex algebras. 5.6: Root lattice vertex algebras and affine vertex algebras. 5.7: Conformal structure for affine vertex algebras. 5.8: Superconformal vertex algebras. 5.9: On classification of conformal superalgebras. Bibliography. Index
1,373 citations
"A new n = 6 superconformal algebra" refers background in this paper
...One can show ([ 3 ] Corollary 4.7) that (ii) follows from the property that L(z) is an energy-momentum field, i.e....
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...Theorem 1.1. ([ 3 , 4]) Let g be a superconformal algebra such that its even part 96 is spanned by L( z ) and currents and its odd part is spanned by fields of conformal weights 12 and 3. Then ~ is isomorphic to one of the following superconformal algebras:...
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...One may find a conjecture on classification of superconformal algebras in [ 3 ] (cf [5])....
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...A rigorous mathematical definition of a superconformal algebra is as follows [ 3 ]....
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TL;DR: In this article, the n -point amplitudes of the U(1) string model with a U (1) colour symmetry were analyzed in detail and it was shown that the critical dimension of this model is D = 2.
312 citations
TL;DR: A complete classification of infinite graded algebras containing a Virasoro subalgebra and additional generators transforming with conformal spin 1 2, 1, or 3 2 is derived in this paper.
73 citations
TL;DR: In this article, a classification of superconformal algebras is given, based on the classification of all connected subgroups of SOn(C) which act transitively on the quadric (v, v) = 1.
Abstract: A classification of “physical” superconformal algebras is given. The list consists of seven algebras: the Virasoro algebra, the Neveu-Schwarz algebra, theN = 2,3 and 4 algebras, the superalgebra of all vector fields on theN = 2 supercircle, and a new algebraCK6 constructed in [3]. The proof relies heavily on the classification of all connected subgroups ofSOn(C) which act transitively on the quadric (v, v) = 1.
61 citations
"A new n = 6 superconformal algebra" refers background in this paper
...Theorem 1.1. ([3, 4 ]) Let g be a superconformal algebra such that its even part 96 is spanned by L( z ) and currents and its odd part is spanned by fields of conformal weights 12 and 3. Then ~ is isomorphic to one of the following superconformal algebras:...
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