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

We study several different types of BPS flows within minimal $\mathcal{N}=1$, $D=7$ supergravity with $\text{SU}(2)$ 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 ${\text{Mkw}}_3$ as well as an ${\text{AdS}}_3$ slicing, write down the corresponding flow equations, and integrate them analytically to obtain many examples of asymptotically ${\mathrm{A}\mathrm{d}\mathrm{S}}_7$ 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 $\mathrm{M}2-\mathrm{M}5$ bound states.