M2-branes on a resolved $C_4/Z_4$

Understand

We write down M2-branes on the resolved $C_4/Z_4$ orbifold space.

• The resolved spatial geometry is such that it interpolates between $R^2\times CP_3$ near the branes and $C_4/Z_4$ asymptotically.
• The near horizon geometry of these branes is a deformation of $AdS_4\times S^7/Z_4$.
• An interesting aspect is that for $k=4$ Chern-Simons theory coupling becomes vanishing near the IR cutoff leading to spontaneous compactification to type IIA.