Antisymmetric tensor field and spontaneous magnetization in holographic duality

A real antisymmetric tensor field was introduced to realize a holographic magnetic ordered phase in our previous papers. However, a more careful analysis shows there is a vector ghost in the model. In this paper we present a modified Lagrangian density for the antisymmetric tensor, which is ghost free and causality is well defined, and keeps all the significant results in the original model qualitatively. We show this modified Lagrangian density could come from the dimensional compactification of p-form field in string/M theory. For static curved space-time, we also prove that this modified model is ghost free and does not violate causality. This new model offers a solid foundation for the application of antisymmetric tensor field in holographic duality, especially for the spontaneous magnetization.