N=2 supersymmetric Janus solutions and flows: from gauged supergravity to M theory

We investigate a family of SU(3) x U(1) x U(1)-invariant holographic flows and Janus solutions obtained from gauged N = 8 supergravity in four dimensions. We give complete details of how to use the uplift formulae to obtain the corresponding solutions in M theory. While the flow solutions appear to be singular from the four-dimensional perspective, we fi nd that the eleven-dimensional solutions are much better behaved and give rise to interesting new classes of compacti fi cation geometries that are smooth, up to orbifolds, in the infra-red limit. Our solutions involve new phases in which M2 branes polarize partially or even completely into M5 branes. We derive the eleven-dimensional supersymmetries and show that the eleven-dimensional equations of motion and BPS equations are indeed satis fi ed as a consequence of their four-dimensional counterparts. Apart from elucidating a whole new class of eleven-dimensional Janus and flow solutions, our work provides extensive and highly non-trivial tests of the recently-derived uplift formulae.