Superisometries of the adS*S Superspace

TL;DR

This work develops a unified $G$-covariant framework for the superisometries of near-horizon $\mathrm{adS}_{p+2}\times \mathrm{S}^{d-p-2}$ superspace, showing how the geometry is preserved by explicit transformations of bosonic and fermionic coordinates together with compensating $H$-transformations. By gauging the superalgebra and solving the $G$-covariant Killing equations to all orders in $\theta$, the authors connect coset-based constructions with supergravity superspace, deriving complete expressions for Killing vectors, Killing spinors, and the corresponding symmetry transformations in both flat and AdS backgrounds. They introduce a Killing-spinor gauge that greatly simplifies the Cartan forms and show how the structure constants of the superalgebra can be interpreted as covariantly constant torsions and curvatures in supergravity, ensuring consistency with the supercoset approach. The results enable a precise handling of BPS brane configurations and offer a path to exploiting superconformal symmetries in the gauge-fixed Green–Schwarz action, with potential impact on AdS/CFT and string spectrum analyses.

Abstract

We find the superisometry of the near-horizon superspace, forming the superconformal algebra. We present here the explicit form of the transformation of the bosonic and fermionic coordinates (as well as the compensating Lorentz-type transformation) which keeps the geometry invariant. We comment on i) the BPS condition of the branes in adS background and ii) significant simplification of superisometries of the gauge-fixed Green-Schwarz action in adS(5)*S(5) background.