$\mathcal{N}=2$ consistent truncations from wrapped M5-branes

TL;DR

This paper develops a formalism for consistent truncations of eleven-dimensional supergravity on six-dimensional manifolds, focusing on $ abla=2$ supersymmetric solutions from wrapped M5-branes, leading to specific five-dimensional supergravity models.

Contribution

It introduces a general algorithm for bosonic truncation ansatzes based on $G_S$ structures and applies it to wrapped M5-brane solutions, identifying the most general consistent truncations.

Findings

Derived explicit truncation ansatz for $ abla=2$ supersymmetric backgrounds.

Constructed 5D supergravity models with specific matter content and gauge groups.

Identified the most general consistent truncations for the studied backgrounds.

Abstract

We discuss consistent truncations of eleven-dimensional supergravity on a six-dimensional manifold $M$, preserving minimal $\mathcal{N}=2$ supersymmetry in five dimensions. These are based on $G_S \subseteq USp(6)$ structures for the generalised $E_{6(6)}$ tangent bundle on $M$, such that the intrinsic torsion is a constant $G_S$ singlet. We spell out the algorithm defining the full bosonic truncation ansatz and then apply this formalism to consistent truncations that contain warped AdS$_5 \times_{\rm w}M$ solutions arising from M5-branes wrapped on a Riemann surface. The generalised $U(1)$ structure associated with the $\mathcal{N}=2$ solution of Maldacena-Nu\~nez leads to five-dimensional supergravity with four vector multiplets, one hypermultiplet and $SO(3)\times U(1)\times \mathbb{R}$ gauge group. The generalised structure associated with "BBBW" solutions yields two vector multiplets, one hypermultiplet and an abelian gauging. We argue that these are the most general consistent truncations on such backgrounds.