On the Unitary Representations of a Class of $N=4$ Superconformal Algebras

Gunaydin, M.; Petersen, J.L.; Taormina, A.; Van Proeyen, Antoine

doi:10.1016/0550-3213(89)90421-5

On the Unitary Representations of a Class of $N=4$ Superconformal Algebras

Dec, 1988

29 pages

Published in:

Nucl.Phys.B 322 (1989) 402

Published: 1989

DOI:

10.1016/0550-3213(89)90421-5

Report number:

CERN-TH-5253-88

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Abstract: (Elsevier)

We derive properties of unitary highest weight representations of the N = 4 superconformal algebras in 2 dimensions, characterized by two SU(2) Kač-Moody subalgebras. For the range 3 ⩽ c < 6 we can prove that we have constructed all unitary highest weight representations. These reduce in N = 2 to the discrete series. For other values of the parameters we derive bounds on the values of h , and we conjecture that these are complete. This is motivated by explicit constructions of representations for various values of the parameters. For the so-called massless representations we do indeed prove that our treatment is complete.

ALGEBRA: CONFORMAL
SUPERSYMMETRY
ALGEBRA: REPRESENTATION
ALGEBRA: KAC-MOODY
SYMMETRY: SU(2)
SYMMETRY: SU(3)
SYMMETRY: SU(N)/SU(N-2)
ALGEBRA: COSET SPACE

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On the Unitary Representations of a Class of N=4N=4N=4 Superconformal Algebras

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On the Unitary Representations of a Class of $N=4$ Superconformal Algebras