Simple variables for AdS$_5 \times S^5$ superspace

TL;DR

This paper introduces a simplified variable framework for describing the AdS$_5 imes S^5$ superspace, embedding it into a linear supergroup representation with quadratic constraints, generalizing previous geometric constructions.

Contribution

It presents a new supersymmetric variable parametrization of AdS$_5 imes S^5$ superspace using linear supergroup representations and quadratic constraints, simplifying the geometric description.

Findings

Provides a linear representation of the superspace variables.

Imposes supersymmetric quadratic constraints for embedding.

Generalizes realisations of AdS$_5$ and S$^5$ spaces.

Abstract

We introduce simple variables for describing the AdS$_5\times S^5$ superspace, i. e. $\frac{PSU(2,2|4)}{SO(4,1)\times SO(5)}$. The idea is to embed the coset superspace into a space described by variables which are in linear (ray) representations of the supergroup $PSU(2,2|4)$ by imposing certain supersymmetric quadratic constraints (up to two overall U(1) factors). The construction can be considered as a supersymmetric generalisation of the elementary realisations of the $AdS_5$ and the $S^5$ spaces by the SO(4,2) and SO(6) invariant quadratic constraints on two six-dimensional flat spaces.