Holography of Dyonic Dilaton Black Branes

TL;DR

The paper investigates holographic dilaton–axion black branes in AdS with both electric and magnetic charges, using SL(2,R) duality to generate dyonic solutions and to compute transport coefficients. It demonstrates Lifshitz-like near-horizon geometries, a vanishing DC longitudinal conductivity in a magnetic field, and a Hall conductance tied to the axion’s attractor value, along with Weidemann–Franz-type relations for thermoelectric and thermal conductivities. The authors also study attractor flows in SL(2,R) and SL(2,Z)-invariant theories, revealing multiple basins of attraction and potential fixed points; they extend the analysis to general dilaton–axion theories without SL(2,R) symmetry, showing parameter regimes with and without IR attractors and highlighting the dependence of transport exponents on model details. Collectively, the work illuminates how holographic dilaton–axion dynamics shape transport, magnetotransport, and IR fixed points, with implications for strongly coupled 2+1D systems under magnetic fields and potential connections to quantum Hall-like phenomena.

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.