Dilaton Domain Walls and Dynamical Systems

TL;DR

This paper analyzes domain wall solutions in dilaton gravity with exponential potentials, revealing their dynamical system structure, exact solutions, and supersymmetry properties, including special cases like Janus solutions and bifurcations.

Contribution

It provides a comprehensive dynamical systems analysis of dilaton domain walls, including exact solutions, bifurcation behavior, and supersymmetry conditions, advancing understanding of these gravitational configurations.

Findings

Exact phase-plane trajectories for $ ext{lambda}=0$

Identification of bifurcation at $ ext{lambda}$ parameter

Supersymmetric flat domain wall solutions for any $ ext{lambda}$

Abstract

Domain wall solutions of $d$-dimensional gravity coupled to a dilaton field $\sigma$ with an exponential potential $\Lambda e^{-\lambda\sigma}$ are shown to be governed by an autonomous dynamical system, with a transcritical bifurcation as a function of the parameter $\lambda$ when $\Lambda<0$. All phase-plane trajectories are found exactly for $\lambda=0$, including separatrices corresponding to walls that interpolate between $adS_d$ and $adS_{d-1} \times\bR$, and the exact solution is found for $d=3$. Janus-type solutions are interpreted as marginal bound states of these ``separatrix walls''. All flat domain wall solutions, which are given exactly for any $\lambda$, are shown to be supersymmetric for some superpotential $W$, determined by the solution.