A New $N = 4$ Superconformal Algebra

TL;DR

The paper introduces a new $N=4$ superconformal algebra derived from contraction of known algebras, featuring a specific Kac-Moody subalgebra and a nonzero central extension, expanding the understanding of superconformal symmetries.

Contribution

It presents a novel $N=4$ superconformal algebra obtained through a contraction process that depends on the central term, which was not previously known.

Findings

New $N=4$ superconformal algebra with specific subalgebra structure

Contains a nonzero central extension

Derived via a contraction of known algebras

Abstract

It is shown that the previously known $N=3$ and $N=4$ superconformal algebras can be contracted consistently by singular scaling of some of the generators. For the later case, by a contraction which depends on the central term, we obtain a new $N=4$ superconformal algebra which contains an $SU(2)\times {U(1)}^4$ Kac-Moody subalgebra and has nonzero central extension.