# Consistent KK truncations for M5-branes wrapped on Riemann surfaces

## TL;DR

This paper develops a consistent reduction of 11-dimensional supergravity on specific surfaces, resulting in a 5D supergravity theory with new solutions and insights into M5-branes wrapped on Riemann surfaces.

## Contribution

It constructs a new consistent KK truncation of D=11 supergravity on Riemann surfaces, revealing new AdS_5 solutions and their relation to M5-branes and dual SCFTs.

## Key findings

- Maximally supersymmetric AdS_5 vacuum for H^2 case
- Two AdS_5 solutions for S^2 case, one new and unstable
- A subtruncation to an N=2 gauged supergravity with specific scalar manifolds

## Abstract

We construct a consistent Kaluza-Klein reduction of $D=11$ supergravity on $\Sigma_2\times S^4$, where $\Sigma_2=S^2,\mathbb{R}^2$ or $H^2$, or a quotient thereof, at the level of the bosonic fields. The result is a gauged $N=4$, $D=5$ supergravity theory coupled to three vector multiplets, with the gauging lying in an $SO(2)\times SE(3)\subset SO(5,3)$ subgroup of the $SO(1,1)\times SO(5,3)$ global symmetry group of the ungauged theory. For $\Sigma_2=H^2$, the $D=5$ theory has a maximally supersymmetric $AdS_5$ vacuum which uplifts to the known solution of $D=11$ supergravity corresponding to M5-branes wrapping a Riemann surface with genus greater than one and dual to an $N=2$ SCFT in $d=4$. For $\Sigma_2=S^2$, we find two $AdS_5$ solutions, one of which is new, and both of which are unstable. There is an additional subtruncation to an $N=2$ gauged supergravity coupled to two vector multiplets, with very special real manifold $SO(1,1)\times SO(1,1)$, and a single hypermultiplet, with quaternionic K\"ahler manifold $SU(2,1)/S[U(2)\times U(1)]$ and gauging associated with an $SO(2)\times\mathbb{R}\subset SU(2,1)$ subgroup.