Holography of Dyonic Dilaton Black Branes

Abstract

We study black branes carrying both electric and magnetic charges in Einstein-Maxwell theory coupled to a dilaton-axion in asymptotically anti de Sitter space. After reviewing and extending earlier results for the case of electrically charged branes, we characterise the thermodynamics of magnetically charged branes. We then focus on dyonic branes in theories which enjoy an $SL(2,R)$ electric-magnetic duality. Using $SL(2,R)$, we are able to generate solutions with arbitrary charges starting with the electrically charged solution, and also calculate transport coefficients. These solutions all exhibit a Lifshitz-like near-horizon geometry. The system behaves as expected for a charged fluid in a magnetic field, with non-vanishing Hall conductance and vanishing DC longitudinal conductivity at low temperatures. Its response is characterised by a cyclotron resonance at a frequency proportional to the magnetic field, for small magnetic fields. Interestingly, the DC Hall conductance is related to the attractor value of the axion. We also study the attractor flows of the dilaton-axion, both in cases with and without an additional modular-invariant scalar potential. The flows exhibit intricate behaviour related to the duality symmetry. Finally, we briefly discuss attractor flows in more general dilaton-axion theories which do not enjoy $SL(2,R)$ symmetry.

56 Pages, 1 figure

References in corpus (16)

• Lectures on Holographic Superfluidity and Superconductivity
• Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes
• Non-relativistic holography
• Hall conductivity from dyonic black holes
• Black holes in asymptotically Lifshitz spacetime
• Ohm's Law at strong coupling: S duality and the cyclotron resonance
• On String Theory Duals of Lifshitz-like Fixed Points
• Fractional Quantum Hall Effect via Holography: Chern-Simons, Edge States, and Hierarchy
• Gravity Dual of a Quantum Hall Plateau Transition
• Quantum criticality and black holes
• SL(2,Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry
• Thermal behavior of charged dilatonic black branes in AdS and UV completions of Lifshitz-like geometries
• Strange Metallic Behavior in Anisotropic Background
• AC Transport at Holographic Quantum Hall Transitions
• Conductivity in the anisotropic background
• Modular Symmetry and Fractional Charges in N=2 Supersymmetric Yang-Mills and the Quantum Hall Effect

Cited by in corpus (5)

• Electron stars for holographic metallic criticality
• Fermi surfaces and gauge-gravity duality
• Holography of charged dilatonic black branes at finite temperature
• Zero Sound in Effective Holographic Theories
• Charged Dilatonic Black Holes and their Transport Properties