Tunneling potentials to nothing

The catastrophic decay of a spacetime with compact dimensions, via bubbles of nothing (BoNs), is probably a generic phenomenon. BoNs admit a four-dimensional description as singular Coleman–de Luccia bounces of the size modulus field, stabilized by some potential $V(\varphi )$. We apply the tunneling potential approach to this 4D description to provide a very simple picture of BoNs. Using it, we identify four different types of BoN, corresponding to different classes of higher-dimensional theories. We also identify 4D theories featuring a new type of quenching of BoN decay, which may be present even for dS vacua, and discuss the viability of embedding such models in a higher-dimensional theory. The present approach allows us to treat in a single framework BoN nucleation and other decay channels, and we study the interplay between the different nonperturbative instabilities comparing their decay rates.

Figure 1

Typical shape of tunneling potentials for the decay of AdS/Minkowski (lower curve) or dS (upper) vacua.

Figure 2

Top: Potential $V={\varphi }^2/2$ and tunneling potentials $V_t(A;\varphi )$ (bounded by $\overline{V_t}$, dashed line). Bottom: Tunneling action $S$ and prefactors $V_{tA}$ and $D_{\infty }$.

Figure 3

Top: Potential [Eq. (26)] with $V_{+}=0$ and tunneling potentials $V_t(A;\varphi )$: $\overline{V_t}$ (black dashed), pseudobounces (green), CdL bounce (red), and BoNs (orange). Bottom: Tunneling action $S$ for the $V_t(A;\varphi )$. For the BoN range of $A$, (rescaled) prefactors $V_{tA}$ and $D_{\infty }$.