Hall conductivity from dyonic black holes

By S. Hartnoll, P. Kovtun. 2007

293 citations recorded by the source corpus.

A class of strongly interacting $2+1$ dimensional conformal field theories in a transverse magnetic field can be studied using the AdS/CFT duality. We compute zero momentum hydrodynamic response functions of maximally supersymmetric $2+1$ dimensional $SU(N)$ Yang-Mills theory at the conformal fixed point, in the large $N$ limit. With background magnetic field $B$ and electric charge density $\ensuremath{\rho}$, the Hall conductivity is found to be $\ensuremath{\rho}/B$. The result, anticipated on kinematic grounds in field theory, is obtained from perturbations of a four-dimensional AdS black hole with both electric and magnetic charges.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0f3f35b556ae67eb27d8c63a92594d847e456cb9

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Citations in the corpus

Building a holographic superconductor. (2008, background): “um ﬁeld theory can be extended to describe aspects of nuclear physics such as the results of heavy ion collisions at RHIC [2] and to certain condensed matter systems. Phenomena such as the Hall eﬀect [3] and Nernst eﬀect [4, 5, 6] have dual gravitational descriptions. One can ask if there is a dual ”
Peculiar properties of a charged dilatonic black hole in AdS 5 (2009, background): “The AdS4-Reissner-Nordstrom black hole was one of the first gravity models to be considered in this context [2, 3, 4].”
Pseudogap and time reversal breaking in a holographic superconductor (2008, background): “[28], in that it is not due to an external magnetic field.”
Magnetic Brane Solutions in AdS (2009, background): “g [1]-[11]) to the study of 2 + 1 gauge theories in magnetic fields.”
Fractional quantum Hall effect via holography: Chern-Simons, edge states and hierarchy (2009, background): “See also [19, 20, 21] for holographic calculations of the classical Hall effect.”
Electron stars for holographic metallic criticality (2010, unknown): “s then determined uniquely to be the planar AdS-Reissner-Nordstrom black hole. This black hole was therefore a natural starting point for investigations into strongly interacting nite density systems [15, 16, 17, 18]. Reviews of this and other earlier work can be found in [8, 9, 19]. 1 A conceptuall”
Holographic Quantum Matter (2016, background): “The ω = 0 limit is especially simple; b+ = −e(2)ρ/Be+ and hence from (384), as first found in [347],”
Holographic Superconductors (2008, background): “The magnetic charge gives the value of the background magnetic field, as explained in, for instance [20].”
Analytic calculation of properties of holographic superconductors (2010, background): “Phenomena such as the Hall effect [10] and Nernst effect [11–13] have also been shown to have dual gravitational descriptions.”
Quantum oscillations and black hole ringing (2009, unknown): “[28, 14]) Ω0 = − AL2 2κ2r3 + ( 1 + r2 +μ 2 γ2 − 3r4 +B 2 γ2 ) , (34)”
Ohm's law at strong coupling: S duality and the cyclotron resonance (2007, methodology): “Thus we recover the result of [6] for the hydrodynamic Hall conductivity, as expected on general kinematic grounds.”
Lectures on holographic superfluidity and superconductivity (2009, unknown): “[30].”
Impure AdS/CFT correspondence (2008, unknown): “In particular, when studying the Nernst effect at ρ = 0 we will find that there is no dependence on γ.”
Charged magnetic brane solutions in AdS5 and the fate of the third law of thermodynamics (2009, methodology): “This brane solution is known analytically for all ρ and B; its spectrum of small fluctuations may be obtained systematically, and used to compute physical quantities such as electric and thermal conductivities [1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12].”
The gravity dual of a p-wave superconductor (2008, background): “More sophisticated examples have been discussed, for example, in [21].”