D3-D7 Holographic dual of a perturbed 3D CFT

TL;DR

This paper uses holographic duality to analyze how perturbations like magnetic fields and Fermion mass influence a 3D defect conformal field theory, revealing phenomena such as magnetic catalysis and deriving key physical properties.

Contribution

It provides a perturbative study of RG flows in a D3-D7 holographic setup, demonstrating magnetic catalysis and deriving formulas for screening length and diamagnetic moment.

Findings

Magnetic catalysis of chiral symmetry breaking at specific flux values

Explicit solutions for RG flow with small Fermion mass and magnetic field

Formulas for Debye screening length and diamagnetic moment

Abstract

An appropriately oriented D3-D7-brane system is the holographic dual of relativistic Fermions occupying a 2+1-dimensional defect embedded in 3+1-dimensional spacetime. The Fermions interact via fields of ${\mathcal N}=4$ Yang-Mills theory in the 3+1-dimensional bulk. Recently, using internal flux to stabilize the system in the probe $N_7<<N_3$ limit, a number of solutions which are dual to conformal field theories with Fermion content have been found. We use holographic techniques to study perturbations of a particular one of the conformal field theories by relevant operators. Generally, the response of a conformal field theory to such a perturbation grows and becomes nonperturbative at low energy scales. We shall find that a perturbation which switches on a background magnetic field $B$ and Fermion mass $m$ induces a renormalization group flow that can be studied perturbatively in the limit of small $m^2/B$. We solve the leading order explicitly. We find that, for one particular value of internal flux, the system exhibits magnetic catalysis, the spontaneous breaking of chiral symmetry enhanced by the presence of the magnetic field. In the process, we derive formulae predicting the Debye screening length of the Fermion-antiFermion plasma at finite density and the diamagnetic moment of the ground state of the Fermion system in the presence of a magnetic field.