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arXiv · hep-th/9902069

Spontaneously Broken Translational Invariance of Compactified Space

M. Sakamoto·M. Tachibana·K. Takenaga
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Abstract

We propose a mechanism to break the translational invariance of compactified space spontaneously. As a simple model, we study a real $ϕ^4$ model compactified on $M^{D-1}\otimes S^1$ in detail, where we impose a nontrivial boundary condition on $ϕ$ for the $S^1$-direction. It is shown that the translational invariance for the $S^1$-direction is spontaneously broken when the radius $R$ of $S^1$ becomes larger than a critical radius $R^*$ and also that the model behaves like a $ϕ^4$ model on a single kink background for $R \to \infty$. It is pointed out that spontaneous breakdown of translational invariance is accompanied by that of some global symmetries, in general, in our mechanism.

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M. Sakamoto, M. Tachibana, K. Takenaga. 1999-02-10. Spontaneously Broken Translational Invariance of Compactified Space. https://doi.org/10.1016/s0370-2693(99)00555-9

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