Conformal symmetry breaking in holographic QCD

TL;DR

This paper explores how conformal symmetry breaking occurs in a holographic QCD model at zero temperature, revealing the emergence of a massless state in spontaneous breaking and its mass dependence when explicitly broken.

Contribution

It introduces a simple holographic model demonstrating conformal symmetry breaking and analyzes the spectrum of states, including the transition from massless to massive states.

Findings

Spontaneous breaking yields a massless scalar state.

Explicit breaking results in a massive scalar state.

Mass of the lightest state depends on conformal dimension.

Abstract

In this paper, we investigate a simple holographic model which describes the conformal symmetry breaking at zero temperature. The model is implemented in the context of effective holographic models for QCD described by the Einstein-dilaton equations. The realization of spontaneous conformal symmetry breaking shows a massless state in the spectrum. The existence of this state is confirmed when we compute the two-point correlation function of the scalar operator in the dual field theory, where it has a pole. On the other hand, when there is an explicit conformal symmetry breaking the massless state becomes massive, which in the dual gravitational theory is related to a deformation of the Anti-de Sitter (AdS) background by a massive scalar (dilaton) field. Moreover, we show the mass dependence on the conformal dimension of the lightest state.