# Non-Supersymmetric Magic Theories and Ehlers Truncations

## TL;DR

This paper explores non-supersymmetric 'magic' theories derived from split division algebras via Ehlers truncations of maximal supergravity, revealing new classes of theories and analyzing black-hole duality orbits.

## Contribution

It introduces a systematic method to obtain non-supersymmetric theories through Ehlers truncations and extends the framework to various $SL(n,\,\mathbb{R})$ cases and non-maximal theories.

## Key findings

- Derived new non-supersymmetric theories from split quaternion and complex algebras.
- Connected Ehlers truncations to very-extended Kac-Moody algebra techniques.
- Analyzed duality orbits of extremal black-hole solutions in these theories.

## Abstract

We consider the non-supersymmetric "magic" theories based on the split quaternion and the split complex division algebras. We show that these theories arise as "Ehlers" $SL(2,\mathbb{R})$ and $SL(3,\mathbb{R})$ truncations of the maximal supergravity theory, exploiting techniques related to very-extended Kac-Moody algebras. We also generalise the procedure to other $SL(n,\mathbb{R})$ truncations, resulting in additional classes of non-supersymmetric theories, as well as to truncations of non-maximal theories. Finally, we discuss duality orbits of extremal black-hole solutions in some of these non-supersymmetric theories.