Chern-Simons Level Shifts and M2-brane Flows

The Chern-Simons level k of ABJM gauge theory captures the orbifolding in the dual geometry. This suggests that if we move the membranes away from the tip of the orbifold to a smooth point, it should trigger an RG flow that changes the level to k = 1. We construct an explicit supergravity solution that is dual to this shift from generic k to k = 1. In the gauge theory side, we present arguments for why this shift is plausible at the end of the RG flow. We also consider a resolution of the orbifold for the case k = 4 (where explicit metrics can be found), and construct the smooth supergravity solution that interpolates between AdS4 × S/Z4 and AdS4 × S, corresponding to localized branes on the blown up six cycle. In the gauge theory, we make some comments about the dimension eight operator dual to the resolution as well as the associated RG flow.