Holography of dyonic dilaton black branes. (English) Zbl 1291.83069
Summary: 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 \(\mathrm{SL}(2,\mathbb R)\) electric-magnetic duality. Using \(\mathrm{SL}(2,\mathbb R)\), 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 \(\mathrm{SL}(2,\mathbb R)\) symmetry.
MSC:
| 83C22 | Einstein-Maxwell equations |
| 83C57 | Black holes |
| 83C30 | Asymptotic procedures (radiation, news functions, \(\mathcal{H} \)-spaces, etc.) in general relativity and gravitational theory |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81T17 | Renormalization group methods applied to problems in quantum field theory |
| 81T10 | Model quantum field theories |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 82C70 | Transport processes in time-dependent statistical mechanics |
Keywords:
gauge-gravity correspondence; black holes in string theory; AdS-CFT correspondence; Chern-Simons theoriesReferences:
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