Boomerang RG flows in M-theory with intermediate scaling

We construct novel RG flows of D=11 supergravity that asymptotically approach $AdS_4\times S^7$ in the UV with deformations that break spatial translations in the dual field theory. In the IR the solutions return to exactly the same $AdS_4\times S^7$ vacuum, with a renormalisation of relative length scales, and hence we refer to the flows as `boomerang RG flows'. For sufficiently large deformations, on the way to the IR the solutions also approach two distinct intermediate scaling regimes, each with hyperscaling violation. The first regime is Lorentz invariant with dynamical exponent $z=1$ while the second has $z=5/2$. Neither of the two intermediate scaling regimes are associated with exact hyperscaling violation solutions of $D=11$ supergravity. The RG flow solutions are constructed using the four dimensional $N=2$ STU gauged supergravity theory with vanishing gauge fields, but non-vanishing scalar and pseudoscalar fields. In the ABJM dual field theory the flows are driven by spatially modulated deformation parameters for scalar and fermion bilinear operators.