Dilaton Domain Walls and Dynamical Systems

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 $ad{S}_d$ 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.

arXiv comment30 pp, 11 figs, significant revision of original. Minor additional corrections in version to appear in journal

References in corpus (16)

• Modeling the fifth dimension with scalars and gravity
• Locally Localized Gravity
• Gravitational Stability and Renormalization-Group Flow
• The domain-wall/QFT correspondence
• A Dilatonic Deformation of AdS_5 and its Field Theory Dual
• Fake Supergravity and Domain Wall Stability
• The dS/dS Correspondence
• Domain Walls from Anti-de Sitter Spacetime
• Multi-Domain Walls in Massive Supersymmetric Sigma-Models
• Liouville and Toda Solitons in M-theory
• Dilatonic p-brane solitons
• Cosmology as Geodesic Motion
• Curved BPS domain wall solutions in five-dimensional gauged supergravity
• Curved BPS domain walls and RG flow in five dimensions
• Bent BPS domain walls of D=5 N=2 gauged supergravity coupled to hypermultiplets
• Flat World of Dilatonic Domain Walls

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• Hamilton-Jacobi method for Domain Walls and Cosmologies
• Recurrent Acceleration in Dilaton-Axion Cosmology
• Domain-wall/Cosmology correspondence in adS/dS supergravity
• Thermal/quantum effects and induced superstring cosmologies
• Pseudo-Supersymmetry and the Domain-Wall/Cosmology Correspondence
• Janus and Multifaced Supersymmetric Theories
• Janus and Multifaced Supersymmetric Theories II
• Hamilton-Jacobi Mechanics from Pseudo-Supersymmetry
• Dual of Big-bang and Big-crunch
• Axion-Dilaton Domain Walls and Fake Supergravity
• Janus within Janus
• Inflationary de Sitter solutions from superstrings
• Massive 3D Gravity Big-Bounce
• BPS Domain Walls and Vacuum Structure of N=1 Supergravity Coupled to a Chiral Multiplet
• Einstein Branes
• AdS-Sliced Flavor Branes and Adding Flavor to the Janus Solution
• Domain Walls in Extended Lovelock Gravity
• Symmetry Breaking Patterns for Inflation
• From Wave Geometry to Fake Supergravity