Quantum critical transport, duality, and M-theory

By Christopher P. Herzog, P. Kovtun, S. Sachdev, D. Son. 2007

359 citations recorded by the source corpus.

We consider charge transport properties of 2+1 dimensional conformal field theories at non-zero temperature. For theories with only Abelian U(1) charges, we describe the action of particle-vortex duality on the hydrodynamic-to-collisionless crossover function: this leads to powerful functional constraints for self-dual theories. For N=8 supersymmetric, SU(N) Yang-Mills theory at the conformal fixed point, exact hydrodynamic-to-collisionless crossover functions of the SO(8) Rcurrents can be obtained in the large N limit by applying the AdS/CFT correspondence to Mtheory. In the gravity theory, fluctuating currents are mapped to fluctuating gauge fields in the background of a black hole in 3+1 dimensional anti-de Sitter space. The electromagnetic self-duality of the 3+1 dimensional theory implies that the correlators of the R-currents obey a functional constraint similar to that found from particle-vortex duality in 2+1 dimensional Abelian theories. Thus the 2+1 dimensional, superconformal Yang Mills theory obeys a “holographic self duality” in the large N limit, and perhaps more generally.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/73a5ea5c8bb570ba248e6cd63636ae489d20b89b

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Citations in the corpus

Ohm's law at strong coupling: S duality and the cyclotron resonance (2007, background): “Such a self-dual field strength does not back react on the geometry and thus must lead to the frequency independent conductivity found in [1].”
Ground states of holographic superconductors (2009, background): “The theory (1) was introduced in [1] with the aim of describing superconducting black holes, following earlier work [2] on black hole phase transitions and [3, 4, 5], among others, on the possible relation between AdS4 vacua and quantum critical behavior.”
ABJM with Flavors and FQHE (2009, methodology): “12) with M = 0 has an S-duality that inverts the Yang-Mills coupling, as was also noted in a different example [24].”
Landscape of superconducting membranes (2009, background): “3 • The electrical conductivity at zero momentum is frequency independent [27] σ ≡ σxx = 1 g2 .”
Holography of charged dilaton black holes (2009, background): “(The transport in such backgrounds has been explored in detail in [15], where in fact the authors argue that σ(ω/T ) is a constant (11)We thank K.”
Lectures on holographic methods for condensed matter physics (2009, background): “Figure taken from [80].”
Quantum magnetism and criticality (2007, background): “(22) and (23), including the exact values [71, 72] of the numbers K, Θ1, Θ2.”
Pseudogap and time reversal breaking in a holographic superconductor (2008, background): “38 98 v2 [”
Introduction to Holographic Superconductors (2010, background): “Above the critical temperature, the conductivity is constant [33].”
The gravity dual of a p-wave superconductor (2008, background): “A surprising result of [23] is that σ̃xx = σ̃yy = 1 for the AdS4-Schwarzschild solution (15), for all ω and T .”
Towards strange metallic holography (2009, background): “The frequency independence here is related to additional symmetries of the Maxwell and DBI actions [39].”
Lectures on holographic non-Fermi liquids and quantum phase transitions (2011, methodology): “8 The application of holographic methods to condensed matter physics was initiated in [48] and other reviews include [49–56].”
A covariant holographic entanglement entropy proposal (2007, neutral): “, [63] for other recent interesting approach).”
Building a holographic superconductor. (2008, background): “quency independent is a characteristic of theories with AdS4 duals [ 15 ].”