Representation theory of the affine Lie superalgebra sl(2/1:C) at fractional level - INSPIRE

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Representation theory of the affine Lie superalgebra sl(2/1:C) at fractional level

P. Bowcock
(
- Durham U.
)
,
A. Taormina
(
- Durham U.
)

May, 1996

27 pages

Published in:

Commun.Math.Phys. 185 (1997) 467-493

e-Print:

hep-th/9605220 [hep-th]

DOI:

10.1007/s002200050099

Report number:

DTP-96-21

View in:

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Abstract:

N=2 noncritical strings are closely related to the \Slr/\Slr Wess-Zumino- Novikov-Witten model, and there is much hope to further probe the former by using the algebraic apparatus provided by the latter. An important ingredient is the precise knowledge of the \hslc representation theory at fractional level. In this paper, the embedding diagrams of singular vectors appearing in \hslc Verma modules for fractional values of the level (

k=p/q-1

, p and q coprime) are derived analytically. The nilpotency of the fermionic generators in \hslc requires the introduction of a nontrivial generalisation of the MFF construction to relate singular vectors among themselves. The diagrams reveal a striking similarity with the degenerate representations of the

N=2

superconformal algebra.

Note:

Latex file, 31pp, 6 epsf figures uufiled Report-no: DTP/96/21

field theory: conformal
dimension: 2
Wess-Zumino-Witten model
algebra: SL(2/1,C)
algebra: affine
supersymmetry: algebra
algebra: representation

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Figures(0)

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