# On supersymmetric AdS6 solutions in 10 and 11 dimensions

## TL;DR

This paper proves non-existence of certain supersymmetric AdS6 solutions in 10 and 11-dimensional supergravity theories, clarifying constraints on internal space topology and flux configurations.

## Contribution

It establishes non-existence theorems for smooth, supersymmetric AdS6 solutions with specific internal space topologies in supergravity theories.

## Key findings

- No solutions with internal space topology F * S^2.
- Internal space admits an so(3) symmetry action.
- Constraints on flux independence and spinor bi-linears.

## Abstract

We prove a non-existence theorem for smooth, supersymmetric, warped AdS6 solutions with connected, compact without boundary internal space in D=11 and (massive) IIA supergravities. In IIB supergravity we show that if such AdS6 solutions exist, then the NSNS and RR 3-form fluxes must be linearly independent and certain spinor bi-linears must be appropriately restricted. Moreover we demonstrate that the internal space admits an so(3) action which leaves all the fields invariant and for smooth solutions the principal orbits must have co-dimension two. We also describe the topology and geometry of internal spaces that admit such a so(3) action and show that there are no solutions for which the internal space has topology F * S^2, where F is an oriented surface.