M2-brane Probe Dynamics and Toric Duality

TL;DR

This paper investigates the dynamics of a single M2-brane in toric Calabi-Yau four-folds using the M-theory crystal model, revealing how the probe theory encodes geometric and duality properties of the underlying space.

Contribution

It introduces an effective abelian gauge theory for M2-brane probes that captures key features of the dual CFT3 and elucidates the role of toric duality and resolutions.

Findings

The moduli space of the gauge theory matches the Calabi-Yau singularity.

The matter charges are given by intersection numbers in the crystal.

Discussion of toric duality and potential RG flows.

Abstract

We study the dynamics of a single M2-brane probing toric Calabi-Yau four-fold singularity in the context of the recently proposed M-theory crystal model of AdS4/CFT3 dual pairs. We obtain an effective abelian gauge theory in which the charges of the matter fields are given by the intersection numbers between loops and faces in the crystal. We argue that the probe theory captures certain aspects of the CFT3 even though the true M2-brane CFT is unlikely to be a usual gauge theory. In particular, the moduli space of vacua of the gauge theory coincides precisely with the Calabi-Yau singularity. Toric duality, partial resolution, and a possibility of new RG flows are also discussed.