A non-reductive N=4 superconformal algebra

Abstract

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 Inönü-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.

10 pages, LaTeX, version to be published

References in corpus (2)

• Comments on N=4 Superconformal Algebras
• Constructing Classical and Quantum Superconformal Algebras on the Boundary of AdS_3

Cited by in corpus (3)

• Galilean contractions of $W$-algebras
• Asymmetric Galilean conformal algebras
• On twisted large N=4 conformal superalgebras