M2-branes on a resolved $C_4/Z_4$

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.

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