M2-branes on a resolved $C_4/Z_4$

TL;DR

This paper constructs M2-brane solutions on a resolved orbifold space, revealing a geometry that interpolates between different spaces and exhibits a spontaneous compactification to type IIA string theory.

Contribution

It provides explicit M2-brane solutions on a resolved $C_4/Z_4$ orbifold, exploring their near horizon geometry and IR behavior, including spontaneous compactification.

Findings

Interpolating geometry between $R^2\times CP_3$ and $C_4/Z_4$

Deformed $AdS_4\times S^7/Z_4$ near horizon

Vanishing Chern-Simons coupling leading to compactification

Abstract

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.