Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vacuum Stability of the wrong sign $(-\phi^{6})$ Scalar Field Theory   We apply the effective potential method to study the vacuum stability of the
bounded from above $(-\phi^{6})$ (unstable) quantum field potential. The
stability ($\partial E/\partial b=0)$ and the mass renormalization
($\partial^{2} E/\partial b^{2}=M^{2})$ conditions force the effective
potential of this theory to be bounded from below (stable). Since bounded from
below potentials are always associated with localized wave functions, the
algorithm we use replaces the boundary condition applied to the wave functions
in the complex contour method by two stability conditions on the effective
potential obtained. To test the validity of our calculations, we show that our
variational predictions can reproduce exactly the results in the literature for
the $\mathcal{PT}$-symmetric $\phi^{4}$ theory. We then extend the applications
of the algorithm to the unstudied stability problem of the bounded from above
$(-\phi^{6})$ scalar field theory where classical analysis prohibits the
existence of a stable spectrum. Concerning this, 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 stable (bounded from below) which is against the classical
predictions of the instability of the theory. We assert that the work presented
here represents the first calculations that advocates the stability of the
$(-\phi^{6})$ scalar potential.

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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg