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Authors
J.R. Espinosa
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The false vacua of some potentials do not decay via Euclidean bounces. This typically happens for tunneling actions with a flat direction (in field configuration space) that is lifted by a perturbation into a sloping valley, pushing the bounce off to infinity. Using three different approaches we find a consistent picture for such decays. In the Euclidean approach the bottom of the action valley consists of a family of pseudo-bounces (field configurations with some key good properties of bounces except extremizing the action). The pseudo-bounce result is validated by minimizing a WKB action in Minkowski space along appropriate paths in configuration space. Finally, the simplest approach uses the tunneling action method proposed recently with a simple modification of boundary conditions.
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We study multi-field tunneling using exact solutions for additive potentials. We introduce a binomial potential with non-integer powers that could be considered a generalization of the $4D$ Fubini instanton potential. Using scaling arguments, we show that for multi-field potentials taller and wider barriers may still lead to a smaller bounce action.
Theories with compact extra dimensions are sometimes unstable to decay into a bubble of nothing -- an instability resulting in the destruction of spacetime. We investigate the existence of these bubbles in theories where the moduli fields that set the size of the extra dimensions are stabilized at a positive vacuum energy -- a necessary ingredient of any theory that aspires to describe the real world. Using bottom-up methods, and focusing on a five-dimensional toy model, we show that four-dimensional de Sitter vacua admit bubbles of nothing for a wide class of stabilizing potentials. We show that, unlike ordinary Coleman-De Luccia tunneling, the corresponding decay rate remains non-zero in the limit of vanishing vacuum energy. Potential implications include a lower bound on the size of compactified dimensions.
The decay rates of quasistable states in quantum field theories are usually calculated using instanton methods. Standard derivations of these methods rely in a crucial way upon deformations and analytic continuations of the physical potential, and on the saddle point approximation. While the resulting procedure can be checked against other semi-classical approaches in some one-dimensional cases, it is challenging to trace the role of the relevant physical scales, and any intuitive handle on the precision of the approximations involved are at best obscure. In this paper, we use a physical definition of the tunneling probability to derive a formula for the decay rate in both quantum mechanics and quantum field theory directly from the Minkowski path integral, without reference to unphysical deformations of the potential. There are numerous benefits to this approach, from non-perturbative applications to precision calculations and aesthetic simplicity.
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An alternative approach to the calculation of tunneling actions, that control the exponential suppression of the decay of metastable phases, is presented. The new method circumvents the use of bounces in Euclidean space by introducing an auxiliary function, a tunneling potential $V_t$ that connects smoothly the metastable and stable phases of the field potential $V$. The tunneling action is obtained as the integral in field space of an action density that is a simple function of $V_t$ and $V$. This compact expression can be considered as a generalization of the thin-wall action to arbitrary potentials and allows a fast numerical evaluation with a precision below the percent level for typical potentials. The method can also be used to generate potentials with analytic tunneling solutions.
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