On the instability of the vacuum in multidimensional scalar theories

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 $\lambda {\varphi }^4$ 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.

arXiv comment25 pages, LaTex, UB-ECM-PF 94/17, 3 figures available on request