Domain walls, near-BPS bubbles, and probabilities in the landscape

TL;DR

This paper develops a comprehensive framework for static BPS domain walls in N=1 supergravity within flux-compactification landscapes, providing a large set of explicit BPS walls interpolating between AdS and Minkowski vacua and demonstrating how uplifting to de Sitter space yields near-BPS bubbles. It derives general BPS gradient-flow equations, formulates the BPS form of the action, and presents concrete examples in KKLT-like, STU, and Calabi–Yau flux models. A key result is that uplifted dS vacua can decay rapidly to collapsing AdS or Minkowski sinks, with universal and parameter-dependent rates that sharply affect the landscape probability flow and eventual measure. The work emphasizes irreversible decay channels as sinks, altering stationary distributions and provoking new perspectives on the wave function of the universe in the string landscape.

Abstract

We develop a theory of static BPS domain walls in stringy landscape and present a large family of BPS walls interpolating between different supersymmetric vacua. Examples include KKLT models, STU models, type IIB multiple flux vacua, and models with several Minkowski and AdS vacua. After the uplifting, some of the vacua become dS, whereas some others remain AdS. The near-BPS walls separating these vacua may be seen as bubble walls in the theory of vacuum decay. As an outcome of our investigation of the BPS walls, we found that the decay rate of dS vacua to a collapsing space with a negative vacuum energy can be quite large. The parts of space that experience a decay to a collapsing space, or to a Minkowski vacuum, never return back to dS space. The channels of irreversible vacuum decay serve as sinks for the probability flow. The existence of such sinks is a distinguishing feature of the landscape. We show that it strongly affects the probability distributions in string cosmology.

Figures (14)

• Figure 1: KKLT potential $V$ (blue upper curve) and ${\cal Z}$ (red curve below) as functions of the modulus. One can see that the potential has an AdS minimum at $\phi = \phi^{*}\simeq 4.09854$ and tends to Minkowski limit at large $\phi$. ${\cal Z}$ is always negative in the interval between AdS and Minkowski vacua. Potential energy density $V$ is shown in units $10^{{-15}} M_{p}^{4}$, whereas the covariantly holomorphic superpotential ${\cal Z}$ is shown in units $10^{{-8}} M_{p}^{3}$.
• Figure 2: The KKLT wall interpolating between the AdS and flat Minkowski space which are at infinite distance from each other in the moduli space. We plot the scalar $\phi$, the covariantly holomorphic superpotential ${\cal Z}$ (in units $10^{{-9}}$), the warp factor $a$ and the curvature $R$ (in units $10^{{-15}}$), all as functions of $r$. Here $r$ is the coordinate of the domain wall configuration given in Eq. (\ref{['typeI']}); we show $r$ in units $10^{7}$.
• Figure 3: Here is the contour plot of the covariantly holomorphic superpotential ${\cal Z}(\phi_1,\phi_2)$ and the gradient flow between the two critical points. ${\cal Z}(\phi_1,\phi_2)$ is everywhere positive between AdS critical points, it vanishes only at the asymptotically Minkowski vacuum.
• Figure 4: Flow of the potential $V(\phi_{1}(r),\phi_{2}(r))$.
• Figure 5: Flow on $\psi$ complex plane.