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LIE SUPERALGEBRAS OF STRING THEORIES

PAVEL GROZMAN, DIMITRY LEITES, IRINA SHCHEPOCHKINA

Abstract

We describe simple complex Lie superalgebras of vector fields on “supercircles” - stringy superalgebras - in intrinsic terms. This is an announcement of a classification: there are four series of such algebras and four exceptional stringy superalgebras.

We also describe Lie superalgebras close to the simple stringy ones, namely, 12 of the simple stringy Lie superalgebras are distinguished: only they have nontrivial central extensions and since one of the distinguished superalgebras has three nontrivial central extensions each, there exist exactly 14 superizations of the Liouville action, Schrödinger equation, KdV hierarchy, etc. We also present the three nontrivial cocycles on the N=4 extended Neveu–Schwarz superalgebra in terms of primary fields.

One of these stringy superalgebras is a Kac–Moody superalgebra g(A) with a nonsymmetrizable Cartan matrix A. It can not be interpreted as a central extension of a twisted loop algebra.

In the literature the stringy superalgebras are often referred to with an unfortunate term superconformal. We show that only three of simple stringy superalgebras are indeed conformal.

Viện Toán học, Viện Hàn lâm Khoa học và Công nghệ Việt Nam

Địa chỉ: Số 18 đường Hoàng Quốc Việt, quận Cầu Giấy, Hà Nội

Điện thoại: 024 37563474 - Fax: 024 37564303

Email: vientoan@math.ac.vn

Viện nghiên cứu cao cấp về toán Hội Toán học Mỹ MathScinet Thư viện số (VAST) Arxiv
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Messages2TimelineExceptionsViews8RouteQueries108Models431MailsGateSessionRequest
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      Metadata
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