BPS objects in D=7 supergravity and their M-theory origin

TL;DR

This paper explores various BPS flow solutions in seven-dimensional supergravity with an SU(2) gauge group, including new analytic and numerical solutions with a running 3-form, and discusses their M-theory origins as M2-M5 bound states.

Contribution

It introduces new classes of BPS flows with a dynamical 3-form and vector fields in D=7 supergravity, providing analytic and numerical solutions and their eleven-dimensional M-theory interpretation.

Findings

Derived analytic solutions for asymptotically AdS7 geometries with a running 3-form.

Numerically integrated flows with non-vanishing vector fields.

Connected solutions to M2-M5 bound states in M-theory.

Abstract

We study several different types of BPS flows within minimal $\mathcal{N}=1$, $D=7$ supergravity with $\textrm{SU}(2)$ gauge group and non-vanishing topological mass. After reviewing some known domain wall solutions involving only the metric and the $\mathbb{R}^{+}$ scalar field, we move to considering more general flows involving a "dyonic" profile for the 3-form gauge potential. In this context, we consider flows featuring a $\textrm{Mkw}_{3}$ as well as an $\textrm{AdS}_{3}$ slicing, write down the corresponding flow equations, and integrate them analytically to obtain many examples of asymptotically $\mathrm{AdS}_7$ solutions in presence of a running 3-form. Furthermore, we move to adding the possibility of non-vanishing vector fields, find the new corresponding flows and integrate them numerically. Finally, we discuss the eleven-dimensional interpretation of the aforementioned solutions as effective descriptions of $\mathrm{M2}-\mathrm{M5}$ bound states.