Supersymmetric Kaluza-Klein reductions of AdS backgrounds

TL;DR

This paper classifies smooth supersymmetric Kaluza-Klein reductions of maximally supersymmetric AdS backgrounds, analyzing their isometries, spin structures, and supersymmetry preservation, providing comprehensive tables of results.

Contribution

It provides a complete classification of one-parameter supersymmetric quotients of AdS backgrounds, including their causal properties and supersymmetry fractions, with detailed tables.

Findings

Classified all smooth spacelike supersymmetric quotients of key AdS backgrounds.

Determined which quotients admit spin structures and their supersymmetry fractions.

Analyzed the causal and spin properties of the orbits of isometry subgroups.

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.