A non-reductive N=4 superconformal algebra

TL;DR

This paper introduces a novel non-reductive N=4 superconformal algebra with 16 generators, derived via contraction from known algebras, expanding the understanding of superconformal symmetries in theoretical physics.

Contribution

It presents the first example of a non-reductive superconformal algebra based on a seven-dimensional Lie algebra, including its structure, subalgebras, and affine extensions.

Findings

Constructed a new N=4 superconformal algebra with 16 generators.

Identified the asymmetric N=4 SCA as a subalgebra.

Classified affine extensions of the non-reductive Lie algebra g.

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 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.