$\mathcal{N}=2$ Supersymmetric Janus Solutions and Flows: From Gauged Supergravity to M Theory

TL;DR

This paper constructs and analyzes new M-theory solutions derived from four-dimensional gauged supergravity, revealing smooth geometries and phases with M2 branes polarizing into M5 branes, thus advancing understanding of holographic flows and Janus solutions.

Contribution

It provides explicit uplift procedures from 4D supergravity to 11D M-theory, discovering new smooth geometries and phases involving brane polarization.

Findings

New classes of smooth eleven-dimensional geometries

Phases with M2 branes polarizing into M5 branes

Validation of uplift formulae through detailed solutions

Abstract

We investigate a family of SU(3)$\times$U(1)$\times$U(1)-invariant holographic flows and Janus solutions obtained from gauged $\mathcal{N}=8$ 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 find that the eleven-dimensional solutions are much better behaved and give rise to interesting new classes of compactification 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 satisfied 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.