Flowing to Higher Dimensions: A New Strongly-Coupled Phase on M2 Branes

TL;DR

This paper introduces a new class of holographic RG flows where M2 branes evolve into intersecting M5 branes, revealing a novel strongly-coupled phase with an emergent extra dimension in the IR, analyzed through supergravity solutions.

Contribution

It constructs a family of holographic flows from M2 to M5 branes, including both supersymmetric and non-supersymmetric cases, with detailed uplift to eleven-dimensional supergravity.

Findings

Flow solutions exhibit dimension 'flow up' from 3D to 4D theories.

Uplifted solutions are regular in eleven dimensions despite singularities in 4D.

Supersymmetry analysis shows M2 supersymmetry polarizes into M5 supersymmetry in IR.

Abstract

We describe a one-parameter family of new holographic RG flows that start from $AdS_4 \times S^7$ and go to $\widehat{AdS_5} \times {\cal B}_6$, where ${\cal B}_6$ is conformal to a K\"ahler manifold and $\widehat{AdS_5}$ is Poincar\'e $AdS_5$ with one spatial direction compactified and fibered over ${\cal B}_6$. 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 Poincar\'e sections of the $\widehat{AdS_5}$ 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.