A non-reductive N=4 superconformal algebra

Details A non-reductive N=4 superconformal algebra A non-reductive N=4 superconformal algebra

2001-08-08

arxiv.org/abs/hep-th/0108054v2

J.Phys.A35:2037-2044,2002

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, LaTeX, version to be published

Scientific paper

10.1088/0305-4470/35/8/316

A new N=4 superconformal algebra (SCA) is presented. Its internal affine Lie algebra is based on the seven-dimensional Lie algebra su(2)\oplus g, where g should be identified with a four-dimensional non-reductive Lie algebra. Thus, it is the first known example of what we choose to call a non-reductive SCA. It contains a total of 16 generators and is obtained by a non-trivial In\"on\"u-Wigner contraction of the well-known large N=4 SCA. The recently discovered asymmetric N=4 SCA is a subalgebra of this new SCA. Finally, the possible affine extensions of the non-reductive Lie algebra g are classified. The two-form governing the extension appearing in the SCA differs from the ordinary Cartan-Killing form.

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