M2-brane Flows and the Chern-Simons Level

TL;DR

This paper constructs supergravity solutions describing RG flows in M2-brane theories that change the Chern-Simons level, illustrating how brane positions influence dual gauge theory dynamics and orbifold resolutions.

Contribution

It provides explicit supergravity solutions for RG flows that alter the Chern-Simons level and explores orbifold resolutions in M2-brane setups, linking geometry to gauge theory dynamics.

Findings

Supergravity solutions for k to 1 level change

Explicit metrics for orbifold resolution at k=4

Insights into dual operators and RG flow mechanisms

Abstract

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 in the IR. 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 X S7/Z4 and AdS4 X S7, corresponding to localized branes on the blown up six cycle. In the gauge theory, we make some comments about the dimension four operator dual to the resolution as well as the associated RG flow.