M2-brane Flows and the Chern-Simons Level

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.

v4: figure with typo replaced, clarifications added. 35 pp

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• Chern-Simons: Fano and Calabi-Yau
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• The Yang-Mills and chiral fields in six dimensions
• More on the scalar-tensor B-F theory
• The D3-probe-D7 brane holographic fractional topological insulator
• BPS operators from the Wilson loop in the 3-dimensional supersymmetric Chern-Simons theory
• Generalized BIons in M-theory
• Fractional black $p$-branes on orbifold ${\mathbb{C}}^n/{\mathbb{Z}}_n$
• Brane Resolution Through Fibration
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