D3-D7 holographic dual of a perturbed 3D CFT

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 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.

Pinning of holographic sliding stripes

“…The D3-D7' model is a holographic model of strongly interacting fermions on a (2 þ 1)-dimensional defect [32], which in many ways resembles graphene [33][34][35]. The construction consists of a probe D7-brane embedded in a D3-brane background such that supersymmetry is completely broken and stabilized by internal magnetic fluxes wrapping 2-cycles in the S 5 .…”

Holographic sliding stripes

“…5 This system was originally designed as a holographic model of the quantum Hall effect because it features a Minkowski embedding at nonzero charge density, yielding a gapped, quantum Hall phase [62,63]. In this paper, we focus instead on the black hole embedding, which is dual to a gapless, conducting quantum fluid [45,46,60,62,67,69].…”

“…In particular, we consider a special case of the background constructed in [60] with zero magnetic field. Under these conditions the corresponding homogeneous state has been argued to resemble graphene [67][68][69]. The possibility of obtaining CDW and SDW phases within graphene-like systems under strong interactions was proposed in [70].…”

Gravity dual of a multilayer system

“…It is clearly an interesting task to find the condensed matter system for which our holographic model could offer a framework for concrete calculations. Each layer effectively mimics graphene, when some of the D5-branes blow up in to D7'-branes [50][51][52][53][54][55][56], so the full multilayer system could perhaps be understood as a (gapped) holographic graphite. More study is needed to make this identification precise.…”