A Kaluza-Klein Model with Spontaneous Symmetry Breaking: Light-Particle Effective Action and its Compactification Scale Dependence

Abstract

We investigate decoupling of heavy Kaluza-Klein modes in an Abelian Higgs model with space-time topologies ${\mathbb{R}}^{3,1}\times S^1$ and ${\mathbb{R}}^{3,1}\times S^1/{\mathbb{Z}}_2$. After integrating out heavy KK modes we find the effective action for the zero mode fields. We find that in the ${\mathbb{R}}^{3,1}\times S^1$ topology the heavy modes do not decouple in the effective action, due to the zero mode of the 5-th component of the 5-d gauge field $A_5$. Because $A_5$ is a scalar under 4-d Lorentz transformations, there is no gauge symmetry protecting it from getting mass and $A_5^4$ interaction terms after loop corrections. In addition, after symmetry breaking, we find new divergences in the $A_5$ mass that did not appear in the symmetric phase. The new divergences are traced back to the gauge-goldstone mixing that occurs after symmetry breaking. The relevance of these new divergences to Symanzik's theorem is discussed. In order to get a more sensible theory we investigate the $S^1/{\mathbb{Z}}_2$ compactification. With this kind of compact topology, the $A_5$ zero mode disappears. With no $A_5$, there are no new divergences and the heavy modes decouple. We also discuss the dependence of the couplings and masses on the compactification scale. We derive a set of RG-like equations for the running of the effective couplings with respect to the compactification scale. It is found that magnitudes of both couplings decrease as the scale $M$ increases. The effective masses are also shown to decrease with increasing compactification scale. All of this opens up the possibility of placing constraints on the size of extra dimensions.

arXiv comment35 pages, 6 figures

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Cited by in corpus (1)

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