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We establish analytically that the potential of N=8 supergravity in fourdimensions has a new N=1 supersymmetric critical point with U(1) x U(1)symmetry. We work within a consistent N=1 supersymmetric truncation and obtainthe holographic flow to this new point from the N=8 critical point. Theoperators that drive the flow in the dual field theory are identified and it issuggested the new critical point might represent a new conformal phase in theholographic fermion droplet models with sixteen supersymmetries. The flow alsohas c_{IR}/c_{UV}} = 1/2. We examine the stability of all twenty known criticalpoints and show that the SO(3) x SO(3) point is a perturbatively stablenon-supersymmetric fixed point. We also locate and describe a novel criticalpoint that also has SO(3)\times SO(3) symmetry and is related to the previouslyknown one by triality in a similar manner to the way that the SO(7)^\pm pointsare related to one another.

New Supersymmetric and Stable, Non-Supersymmetric Phases in Supergravity and Holographic Field Theory