Quantum Deformed $su(m|n)$ Algebra and Superconformal Algebra on Quantum Superspace

TL;DR

This paper explores a quantum-deformed superalgebra on superspace, constructing a deformed superconformal algebra and deriving related deformed spacetime symmetries, revealing new algebraic structures in quantum supersymmetry.

Contribution

It introduces a novel quantum deformation of the $su(m|n)$ algebra on superspace and constructs a corresponding deformed superconformal algebra with applications to spacetime symmetries.

Findings

Deformed $su(m|n)$ algebra on quantum superspace is explicitly constructed.

Deformed superconformal algebra is developed from the deformed $su(1|4)$ algebra.

Derived deformed Lorentz, Minkowski, and supersymmetric algebras as subalgebras.

Abstract

We study a deformed $su(m|n)$ algebra on a quantum superspace. Some interesting aspects of the deformed algebra are shown. As an application of the deformed algebra we construct a deformed superconformal algebra. {}From the deformed $su(1|4)$ algebra, we derive deformed Lorentz, translation of Minkowski space, $iso(2,2)$ and its supersymmetric algebras as closed subalgebras with consistent automorphisms.