# Consistent $S^3$ reductions of six-dimensional supergravity

## TL;DR

This paper derives consistent reductions of six-dimensional supergravity theories to three dimensions, providing explicit formulas and uplifting examples for AdS$_3$ vacua, advancing understanding of supergravity compactifications.

## Contribution

It presents the full non-linear Kaluza-Klein reduction formulas for two six-dimensional supergravity theories to three dimensions, including explicit uplift examples.

## Key findings

- Explicit consistent reduction formulas derived.
- Inequivalent three-dimensional gauged supergravities identified.
- Explicit uplift examples of AdS$_3$ vacua provided.

## Abstract

We work out the consistent AdS$_3\times S^3$ truncations of the bosonic sectors of both the six-dimensional ${\cal N}=(1,1)$ and ${\cal N}=(2,0)$ supergravity theories. They result in inequivalent three-dimensional half-maximal ${\rm SO}(4)$ gauged supergravities describing 32 propagating bosonic degrees of freedom apart from the non-propagating supergravity multiplet. We present the full non-linear Kaluza-Klein reduction formulas and illustrate them by explicitly uplifting a number of AdS$_3$ vacua.