We show that eleven dimensional supergravity in Euclidean signature admits an
exact classical solution with isometry corresponding to a three dimensional
scale invariant field theory without conformal invariance. We also construct
the holographic renormalization group flow that connects the known UV conformal
fixed point and the new scale invariant but not conformal fixed point. In view
of holography, the existence of such classical solutions suggests that the
topologically twisted M2-brane gauge theory possesses a scale invariant but not
conformal phase.