Spontaneously Broken Translational Invariance of Compactified Space

Abstract

We propose a mechanism to break the translational invariance of compactified space spontaneously. As a simple model, we study a real ${\varphi }^4$ model compactified on $M^{D-1}\otimes S^1$ in detail, where we impose a nontrivial boundary condition on $\varphi$ 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 $R^{\ast }$ and also that the model behaves like a ${\varphi }^4$ 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.

9 pages, No figure

References in corpus (1)

• Spontaneous Supersymmetry Breaking from Extra Dimensions

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