A Review of Magnetic Phenomena in Probe-Brane Holographic Matter

Abstract

Gauge/gravity duality is a useful and efficient tool for addressing and studying questions related to strongly interacting systems described by a gauge theory. In this manuscript we will review a number of interesting phenomena that occur in such systems when a background magnetic field is turned on. Specifically, we will discuss holographic models for systems that include matter fields in the fundamental representation of the gauge group, which are incorporated by adding probe branes into the gravitational background dual to the gauge theory. We include three models in this review: the D3-D7 and D4-D8 models, that describe four-dimensional systems, and the D3-D7' model, that describes three-dimensional fermions interacting with a four-dimensional gauge field. *

Spontaneous Electromagnetic Superconductivity of Vacuum in a Strong Magnetic Field: Evidence from the Nambu–Jona-Lasinio Model

“…Both the ρ mesons in QCD, the gluons in Yang-Mills theory, and the W bosons in the electroweak model have the anomalously large g-factor, g ≈ 2. Notice, that the phase diagrams of QCD at finite density (at finite chemical and/or isospin potential) contain certain phases characterized by the presence of exotic vector condensates [9,29,30,31]. Some of these phases exhibit superconducting/superfluid behavior [30,31].…”

“…In terms of the nontrivial condensates 9 , the potential term in the scalar part of the action has the following (renormalized) form:…”

“…In a finite-density (quark) matter the magnetic catalysis [1] may be reversed [8] and the phase diagram may be modified substantially [8,9]. In the absence of matter (i.e., in the vacuum), the external magnetic field affects the finite-temperature phase structure of the theory by shifting the critical temperatures and altering the strength of the confinement-deconfinement and chiral transitions [2,3].…”

Spontaneous electromagnetic superconductivity induced by a strong magnetic field: QCD and electroweak theory

“…Indeed, one can show that, surprisingly, the neutral currents J Z µ of the Z bosons (11) and the neutral current J (0) µ of the ρ mesons (14), satisfy London relations as well:…”

“…The corresponding effective action contains massive vector fields coupled to the massless 1 We would like to stress that we consider pure vacuum only. If matter is present then many other interesting effects may arise: an electric current may be generated along the magnetic field axis in the chirallyimbalanced matter [8] ("the chiral magnetic effect" [9]), the magnetization (electric polarization) of the quark media may depend on electric (magnetic) field background ("the magnetoelectric effect" [10]), the chiral symmetry breaking may be weakened at some density range ("the inverse magnetic catalysis" [11]), and the phase diagram may contain unusual phases exhibiting color superconductivity [12], and phases with certain vector condensates [13,14], including the superfluid/superconducting ones [14]. photon, resembling strongly EW theory for which a magnetic phase transition was found in Ref.…”