Holography of Dyonic Dilaton Black Branes

TL;DR

This paper investigates dyonic black branes in anti-de Sitter space within Einstein-Maxwell-dilaton theories, exploring their thermodynamics, duality transformations, near-horizon geometries, and transport properties like Hall conductance and cyclotron resonance.

Contribution

It extends previous work by characterizing magnetically charged branes, applying $SL(2,R)$ duality to generate dyonic solutions, and analyzing their transport and attractor flow properties.

Findings

Solutions exhibit Lifshitz-like near-horizon geometry.

DC Hall conductance relates to the axion's attractor value.

System shows cyclotron resonance proportional to magnetic field.

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.