Janus and Hades in M-theory

Abstract

Multi-parametric and analytic families of four-dimensional AdS 3 × R (Janus) and AdS 3 × R + (Hades) solutions are constructed in the SO(8) gauged supergravity that arises from the consistent reduction of eleven-dimensional supergravity on S 7 . The solutions are generically non-supersymmetric, involve non-trivial running scalars and preserve a U(1) 4 symmetry. Different patterns of (super) symmetry enhancement occur upon suitable adjustment of the free parameters which further control the boundary conditions of the running scalars. We concentrate on the non-supersymmetric Janus and Hades solutions with SU(3) × U(1) 2 symmetry and provide their higher-dimensional description in terms of M-theory fluxes and membranes. Special attention is paid to a class of such Hades solutions dubbed "ridge flows" which resemble dielectric rotations of Coulomb branch flows previously investigated in the literature.

S-folds and AdS3 flows from the D3-brane

“…Flows of this type can be constructed for which the singularity occurs at a finite radial distance, although we are not investigating them in this work. As mentioned in the introduction, these are the counterparts of the flows to Hades investigated in [6,7].…”

“…the gauging in four dimensions [25,41]. 2 However, and unlike for standard Janus solutions in type IIB [19] and M-theory [6,7], this time there is no maximally supersymmetric round vacuum of the form AdS 4 × S 1 × S 5 that can serve as an endpoint on each side of the Janus solution. 3 This implies that there is no maximally supersymemtric AdS 4 vacuum at the origin of the scalar potential of the effective [SO(1, 1) × SO(6)] R 12 gauged supergravity.…”

“…In addition there are also singular solutions (akin to the flows to Hades discussed in [6,7]) which diverge at some finite value of the radial direction. All together, these three classes of solutions are the analogue of the Janus solutions in the SO(8) [8] and ISO(7) [42][43][44] maximal supergravities constructed in [6,7] and [45,46], respectively.…”

“…However, Janus solutions have been generalised to theories without a dilaton field so that they are solely characterised by the first property. Examples are the Janus solutions of [6,7] constructed in the four-dimensional SO(8) maximal supergravity that arises upon consistent truncation of eleven-dimensional supergravity on a seven-sphere [8,9]. In this work we will relax the first property and investigate regular Janus-type solutions featuring an AdS d−2 space-time geometry that asymptotes to an AdS d geometry on each side of the solution.…”