QCD Vacuum Properties in a Magnetic Field from AdS/CFT: Chiral Condensate and Goldstone Mass

TL;DR

This paper investigates how an external magnetic field affects the chiral condensate and eta' meson mass spectrum using a holographic AdS/CFT model, revealing a quadratic dependence of the condensate on the magnetic field.

Contribution

It demonstrates that within the D3/D7 AdS/CFT model, the chiral condensate exhibits a quadratic dependence on magnetic field, contrasting with the linear dependence predicted by chiral perturbation theory.

Findings

Chiral condensate depends quadratically on magnetic field in the model.

The quadratic dependence aligns with leading-order large N_c analysis.

Chiral perturbation theory's linear dependence is 1/N_c suppressed.

Abstract

Chiral condensate and $\eta^\prime$ meson mass spectrum are studied under the influence of an external Abelian magnetic field. We work within the D3/D7 Karch--Katz model of flavoured AdS/CFT with supersymmetry broken by the Constable--Myers deformation of the metric. It is shown that this setting yields a quadratic dependence of condensate on field, rather than the non-analytic (linear in field) dependence, typical for chiral perturbation theory in the exact chiral limit. We argue that the analytic (quadratic) result must be put into correspondence with the leading-order in the $1/N_c$ decomposition for the condensate, whereas the existing chiral perturbation theory result, which is linear in field strength, is $1/N_c$ suppressed.