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The one-loop effective potential in a scalar theory with quartic interaction on the spaceM 4×T n forn=2 is calculated and is shown to be unbounded from below. This is an indication of a possible instability of the vacuum of theλψ 4 model onM 4, when it is regarded as a low-energy sector of the theory obtained by dimensional reduction of the original six-dimensional one. It is argued that, in some range of the values of the parameters of the theory, higher-loop corrections do not change this result qualitatively. The issue of stability for other values of the numbern of extra dimensions is also discussed.

On the instability of the vacuum in multidimensional scalar theories