# On SUSY-breaking Moduli Spaces of AdS$_7$ Vacua and 6D SCFTs

## TL;DR

This paper investigates supersymmetric AdS7 vacua in massive type IIA string theory, demonstrating their rigidity against supersymmetry-breaking deformations and implications for the conformal manifold of dual 6D theories.

## Contribution

It proves that certain AdS7 vacua without D8-brane charges cannot be deformed to break supersymmetry, indicating the dual 6D theories lack a conformal manifold.

## Key findings

- No supersymmetry-breaking deformations for these vacua
- Dual 6D theories do not have a conformal manifold
- Supports the conjecture that non-supersymmetric AdS vacua are in the swampland

## Abstract

We study supersymmetric AdS$_7$ vacua of massive type IIA string theory, which were argued to describe the near-horizon limit of NS5/D6/D8-brane intersections and to be holographically dual to 6D $(1,0)$ theories. We show, for the case without D8-brane charges, that such vacua do not admit any supersymmetry-breaking deformations. Our result implies that the dual $(1,0)$ theories do not have a conformal manifold, thus extending previously known results for supersymmetric deformations. It is also in line with the recent conjecture that non-supersymmetric AdS vacua are in the swampland.