Isometries in anti-de Sitter and Conformal Superspaces

TL;DR

This paper derives explicit superisometry transformations for various supercoset manifolds, including AdS_5 x S^5 and conformal superspaces, and shows how these reduce to superconformal transformations at the AdS boundary.

Contribution

It provides explicit formulas for superisometries in supercosets with fermionic stability groups and demonstrates their reduction to superconformal transformations at the boundary.

Findings

Superisometries explicitly derived for multiple supercosets.

At AdS boundary, superisometries reduce to N=4 superconformal transformations.

Half of the fermionic coordinates decouple from the superisometries.

Abstract

We derive explicit forms for the superisometries of a wide class of supercoset manifolds, including those with fermionic generators in the stability group. We apply the results to construct the action of SU(2,2|4) on three supercoset manifolds: (10|32)-dimensional AdS_5 x S^5 superspace, (4|16)-dimensional conformal superspace, and a novel (10|16)-dimensional conformal superspace. Using superembedding techniques, we show, to lowest non-trivial order in the fermions, that at the boundary of AdS_5, the superisometries of the AdS_5 x S^5$ superspace reduce to the standard N=4 superconformal transformations. In particular, half of the 32 fermionic coordinates decouple from the superisometries.