# Non-duality in three dimensions

## TL;DR

This paper explores compactifications of M-theory and heterotic string theory to lower dimensions, revealing new supergravity theories, duality obstructions, and a no-go theorem regarding supersymmetry preservation in heterotic models.

## Contribution

It introduces a new class of massive supergravities from M-theory on K3, analyzes dual heterotic descriptions, and proves a no-go theorem about supersymmetry in heterotic compactifications.

## Key findings

- Massive supergravities from M-theory on K3 are identified.
- Obstructions to heterotic duals with geometric descriptions are discussed.
- A no-go theorem shows heterotic geometries preserving 6 supercharges must preserve 8.

## Abstract

We investigate M-theory and heterotic compactifications to 7 and 3 dimensions. In 7 dimensions we discuss a class of massive supergravities that arise from M-theory on K3 and point out obstructions to realizing these theories in a dual heterotic framework with a geometric description. Taking M-theory further down to 3 dimensions on K3xK3 with a choice of flux leads to a rich landscape of theories with various amounts of supersymmetry, including those preserving 6 supercharges. We explore possible heterotic realizations of these vacua and prove a no--go theorem: every heterotic geometry that preserves 6 supercharges preserves 8 supercharges.