Supersymmetric Kaluza-Klein reductions of AdS backgrounds

TL;DR

The paper develops a comprehensive framework to classify smooth Kaluza–Klein quotients of maximally supersymmetric AdS×S Freund–Rubin backgrounds by one-parameter isometry subgroups. It combines an explicit adjoint-orbit analysis of SO(2,p) with spin-structure criteria and a Killing-spinor equivariance test to determine which quotients are smooth, spin, and preserve any supersymmetry. The authors exhaustively enumerate supersymmetric quotients for AdS_3×S^3, AdS_4×S^7, AdS_5×S^5, and AdS_7×S^4, providing detailed blocks, weights, and the resulting SUSY fractions in tables. This work yields a robust geometric toolkit for constructing fluxbrane-like backgrounds and studying near-horizon quotient geometries, with implications for AdS/CFT and string/M-theory time-dependent backgrounds.

Abstract

This paper contains a classification of smooth Kaluza--Klein reductions (by one-parameter subgroups) of the maximally supersymmetric anti de Sitter backgrounds of supergravity theories. We present a classification of one-parameter subgroups of isometries of anti de Sitter spaces, discuss the causal properties of their orbits on these manifolds, and discuss their action on the space of Killing spinors. We analyse the problem of which quotients admit a spin structure. We then apply these results to write down the list of smooth everywhere spacelike supersymmetric quotients of AdS_3 x S^3 (x R^4), AdS_4 x S^7, AdS_5 x S^5 and AdS_7 x S^4, and the fraction of supersymmetry preserved by each quotient. The results are summarised in tables which should be useful on their own. The paper also includes a discussion of supersymmetry of singular quotients.