Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-12-25
Physics
High Energy Physics
High Energy Physics - Theory
17 pages, 9figures. In this version we studied the general theory in d space-time dimensions
Scientific paper
In this work, we show that stability of a theory can not be predicted from classical analysis. Regarding this, we study the stability of the bounded from above $(-\phi^{6})$ scalar field theory where classical analysis prohibits the existence of a stable spectrum. We calculated the effective potential up to first order in the couplings in $d$ space-time dimensions. We find that a Hermitian effective theory is instable while a non-Hermitian but $\mathcal{PT}$-symmetric effective theory characterized by a pure imaginary vacuum condensate is rather stable (bounded from below) which is against the classical predictions of the instability of the theory. This is the first calculations that advocates the stability of the $(-\phi^{6})$ scalar potential. Apart from these interesting results, we showed that the effective field approach we followed is able to reproduce the very recent results presented in Physical Review Letters 105, 031601 (2010) for the corresponding bounded from below theory.
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