Lie superalgebras of string theories
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.
- Publication:
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arXiv e-prints
- Pub Date:
- February 1997
- DOI:
- 10.48550/arXiv.hep-th/9702120
- arXiv:
- arXiv:hep-th/9702120
- Bibcode:
- 1997hep.th....2120G
- Keywords:
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- High Energy Physics - Theory;
- Mathematics - Representation Theory
- E-Print:
- 22 pages, LaTeX