Antisymmetric tensor field and spontaneous magnetization in holographic duality

TL;DR

This paper refines a holographic model using an antisymmetric tensor field by removing ghosts and ensuring causality, thus providing a more solid foundation for studying spontaneous magnetization in holographic duality.

Contribution

It introduces a ghost-free, causality-preserving modified Lagrangian for the antisymmetric tensor field derived from string theory, enhancing the model's physical consistency.

Findings

The modified Lagrangian is ghost free and causal in static curved spacetime.

The model retains key results of the original in describing magnetic phases.

Derived from string/M-theory compactification.

Abstract

A real anti-symmetric tensor field was introduced to realize a holographic magnetic ordered phase in our previous works. 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 anti-symmetric 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 dose 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.