IIB solutions with N>28 Killing spinors are maximally supersymmetric

TL;DR

This paper proves that in IIB supergravity, any background with more than 28 Killing spinors must be maximally supersymmetric, revealing a sharp boundary at 28 supersymmetries.

Contribution

It establishes that all IIB backgrounds with over 28 Killing spinors are necessarily maximally supersymmetric, clarifying the structure of supersymmetric solutions.

Findings

Supercovariant curvature vanishes for N>28 backgrounds

All such backgrounds are maximally supersymmetric

Quotients of maximally supersymmetric backgrounds preserve all 32 or fewer than 29 supersymmetries

Abstract

We show that all IIB supergravity backgrounds which admit more than 28 Killing spinors are maximally supersymmetric. In particular, we find that for all N>28 backgrounds the supercovariant curvature vanishes, and that the quotients of maximally supersymmetric backgrounds either preserve all 32 or N<29 supersymmetries.