Thick domain walls and singular spaces

TL;DR

This paper explores thick domain walls connecting spaces with naked singularities, analyzing their physical relevance via the AdS/CFT correspondence, and examines graviton spectra with exact solutions and boundary conditions.

Contribution

It provides explicit models of thick domain walls with various geometries and analyzes their graviton spectra, including the effects of boundary conditions, linking to holographic principles.

Findings

Exact solutions for flat domain walls and graviton spectra.

Presence of a mass gap in some continuum states.

Boundary conditions can eliminate continuum graviton states.

Abstract

We discuss thick domain walls interpolating between spaces with naked singularities and give arguments based on the $AdS$/CFT correspondence why such singularities may be physically meaningful. Our examples include thick domain walls with Minkowski, de Sitter, and anti-de Sitter geometries on the four-dimensional slice. For flat domain walls we can solve the equivalent quantum mechanics problem exactly, which provides the spectrum of graviton states. In one of the examples we discuss, the continuum states have a mass gap. We compare the graviton spectra with expectations from the $AdS$/CFT correspondence and find qualitative agreement. We also discuss unitary boundary conditions and show that they project out all continuum states.