Flowing to higher dimensions: a new strongly-coupled phase on M2 branes

We describe a one-parameter family of new holographic RG flows that start from AdS ₄ × S ⁷ and go to widehat{Ad{S}_5}× {B}6 , where {B}6 is conformal to a Kähler manifold and widehat{Ad{S}_5} is Poincaré AdS ₅ with one spatial direction compactified and fibered over {B}6 . The new solutions "flow up dimensions," going from the (2 + 1)-dimensional conformal field theory on M2 branes in the UV to a (3 + 1)-dimensional field theory on intersecting M5 branes in the infra-red. The M2 branes completely polarize into M5 branes along the flow and the Poincaré sections of the widehat{Ad{S}_5} are the (3 + 1)-dimensional common intersection of the M5 branes. The emergence of the extra dimension in the infra-red suggests a new strongly-coupled phase of the M2 brane and ABJM theories in which charged solitons are becoming massless. The flow solution is first analyzed by finding a four-dimensional {N}=2 supersymmetric flow in {N}=8 gauged supergravity. This is then generalized to a one parameter family of non-supersymmetric flows. The infra-red limit of the solutions appears to be quite singular in four dimensions but the uplift to eleven-dimensional supergravity is remarkable and regular (up to orbifolding). Our construction is a non-trivial application of the recently derived uplift formulae for fluxes, going well beyond the earlier constructions of stationary points solutions. The eleven-dimensional supersymmetry is also analyzed and shows how, for the supersymmetric flow, the M2-brane supersymmetry in the UV is polarized entirely into M5-brane supersymmetry in the infra-red.