A Soft-Wall Dilaton

TL;DR

This paper investigates the properties of the dilaton in a soft-wall background, demonstrating how different solutions can produce a naturally light dilaton through spontaneous conformal symmetry breaking and nearly-marginal deformations.

Contribution

It introduces new analytic solutions for the dilaton in soft-wall backgrounds, showing how to obtain a naturally light dilaton from nearly-marginal CFT deformations.

Findings

Analytic solutions describing a light dilaton in soft-wall backgrounds.

A mechanism for naturally light dilaton generation via nearly-marginal deformations.

Connection between scalar potential transitions and dilaton mass spectrum.

Abstract

We study the properties of the dilaton in a soft-wall background using two solutions of the Einstein equations. These solutions contain an asymptotically AdS metric with a nontrivial scalar profile that causes both the spontaneous breaking of conformal invariance and the generation of a mass gap in the particle spectrum. We first present an analytic solution, using the superpotential method, that describes a CFT spontaneously broken by a finite dimensional operator in which a light dilaton mode appears in the spectrum. This represents a tuning in the vanishing of the quartic coupling in the effective potential that could be naturally realised from an underlying supersymmetry. Instead, by considering a generalised analytic scalar bulk potential that quickly transitions at the condensate scale from a walking coupling in the UV to an order-one $\beta$-function in the IR, we obtain a naturally light dilaton. This provides a simple example for obtaining a naturally light dilaton from nearly-marginal CFT deformations in the more realistic case of a soft-wall background.