(Un)Higgsing the M2-brane

Abstract

We study various aspects of $ \mathcal{N} = 2 $ quiver-Chern-Simons theories, conjectured to be dual to M2-branes at toric Calabi-Yau four-fold singularities, under Higgsing. In particular we study in detail the orbifold $ {{{\mathbb{C}^4}} \mathord{\left/{\vphantom {{{\mathbb{C}^4}} {\mathbb{Z}_2^3}}} \right.} {\mathbb{Z}_2^3}} $ , obtaining a number of different quiver-Chern-Simons phases for this model, and all 18 toric partial resolutions thereof. In the process we develop a general un-Higgsing algorithm that allows one to construct quiver-Chern-Simons theories by blowing up, thus obtaining a plethora of new models. In addition we explain how turning on torsion G-flux non-trivially affects the supergravity dual of Higgsing, showing that the supergravity and field theory analyses precisely match in an example based on the Sasaki-Einstein manifold $ {Y^{1,2}}\left( {\mathbb{C}{\mathbb{P}^2}} \right) $ .