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On the instability of the vacuum in multidimensional scalar theories

E. Elizalde·K. Kirsten·Yu. Kubyshin
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Abstract

The 1-loop effective potential in a scalar theory with quartic interaction on the space $M^{4} \times T^{n}$ for $n=2$ is calculated and is shown to be unbounded from below. This is an indication of a possible instability of the vacuum of the $λϕ^{4}$ theory on $M^{4}$, when it is regarded as a result of the dimensional reduction of the original six-dimensional model. The issue of stability for other values of the number $n$ of extra dimensions is also discussed.

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E. Elizalde, K. Kirsten, Yu. Kubyshin. 1994-10-14. On the instability of the vacuum in multidimensional scalar theories. https://arxiv.org/abs/hep-th/9410101

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