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.
Highlights
Introducing a nearly massless bulk scalar field
Using the superpotential method we first derive an analytic solution of the coupled Einstein-scalar equations of motion with an asymptotically AdS metric and nontrivial scalar profile that grows in the IR
This is a consequence of using an analytic superpotential and presumably the tuning could be understood from an underlying supersymmetry
Summary
The general 5D action is given by. UV where M is the 5D Planck scale and V (φ) is the bulk scalar potential. The UV brane has an induced metric γ, a brane potential U(φ) and [K] represents the jump in the extrinsic curvature. The requirement of 4D Poincare invariance leads to the usual metric ansatz ds2 = gMN dxM dxN = A2(y)ημν dxμdxν + dy2,. Where the indices M, N = (μ, 5), A(y) is the warp factor and ημν = diag(−1, +1, +1, +1) is the 4D Minkowski metric. The scalar profile φ = φ(y) will in general be a nontrivial function of the 5th coordinate, y. The bulk equations of motion for the metric and scalar profile are given by φ (y) = W (φ),
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