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Quantum Criticality via Magnetic Branes

  • Chapter
Strongly Interacting Matter in Magnetic Fields

Part of the book series: Lecture Notes in Physics ((LNP,volume 871))

Abstract

Holographic methods are used to investigate the low temperature limit, including quantum critical behavior, of strongly coupled 4-dimensional gauge theories in the presence of an external magnetic field, and finite charge density. In addition to the metric, the dual gravity theory contains a Maxwell field with Chern-Simons coupling. In the absence of charge, the magnetic field induces an RG flow to an infrared \(\mathit{AdS}_{3} \times {\bf R}^{2}\) geometry, which is dual to a 2-dimensional CFT representing strongly interacting fermions in the lowest Landau level. Two asymptotic Virasoro algebras and one chiral Kac-Moody algebra arise as emergent symmetries in the IR. Including a nonzero charge density reveals a quantum critical point when the magnetic field reaches a critical value whose scale is set by the charge density. The critical theory is probed by the study of long-distance correlation functions of the boundary stress tensor and current. All quantities of major physical interest in this system, such as critical exponents and scaling functions, can be computed analytically. We also study an asymptotically AdS 6 system whose magnetic field induced quantum critical point is governed by an IR Lifshitz geometry, holographically dual to a D=2+1 field theory. The behavior of these holographic theories shares important similarities with that of real world quantum critical systems obtained by tuning a magnetic field, and may be relevant to materials such as Strontium Ruthenates.

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Notes

  1. 1.

    Einstein indices μ,ν=0,1,2,3 will be used in 3+1-dimensions, while Einstein indices M,N=0,1,2,3,4 will be used in 4+1-dimensions. Our conventions are g=−det(g MN ), as well as \(R^{L}{}_{\mathit{MNK}} = \partial _{K} \varGamma^{L}_{\mathit{MN}} - \partial _{N} \varGamma^{L}_{\mathit{MK}} +\varGamma^{P}_{\mathit{MN}} \varGamma^{L}_{\mathit{KP}} - \varGamma^{P}_{\mathit{MK}}\varGamma^{L}_{\mathit{NP}}\) with R MN =R L MLN and R=g MN R MN .

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Acknowledgements

This work was supported in part by NSF grant PHY-07-57702.

During the course of this entire project, we have benefited from helpful conversations and correspondence with several colleagues, and we wish to thank here Vijay Balasubramanian, David Berenstein, Sudip Chakravarty, Geoffrey Compère, Jan de Boer, Frédéric Denef, Stéphane Detournay, Tom Faulkner, Jerome Gauntlett, Sean Hartnoll, Gary Horowitz, Finn Larsen, Alex Maloney, Eric Perlmutter, Joe Polchinski, Matt Roberts, Joan Simon, and especially Akhil Shah who collaborated on one of our papers. During parts of this work, we have enjoyed the hospitality of the KITP during the “Quantum Criticality and AdS/CFT Correspondence” program in 2009, and of the Aspen Center for Physics in 2011. One of us (E.D.) wishes to thank the Laboratoire de Physique Théorique de l’Ecole Normale Supérieure, and the Laboratoire de Physqiue Théorique et Hautes Energies, CNRS and Université Pierre et Marie Curie—Paris 6, and especially Constantin Bachas and Jean-Bernard Zuber for their warm hospitality while part of this work was being completed.

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of California, Los Angeles, CA, 90095, USA

    Eric D’Hoker & Per Kraus

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  1. Eric D’Hoker
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  2. Per Kraus
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Correspondence to Eric D’Hoker .

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Editors and Affiliations

  1. Department of Physics, Stony Brook University, Nicolls Rd 100, Stony Brook, 11794, New York, USA

    Dmitri Kharzeev

  2. Instituto de Fisica Teorica UAM/CSIC, Universidad Autonoma de Madrid, Nicolas Cabrera 13-15, Madrid, 28049, Spain

    Karl Landsteiner

  3. Institut für Theoretische Physik, Technische Universität Wien, Wiedner Haupstr. 8, Wien, 1040, Austria

    Andreas Schmitt

  4. Physics Department (MC 273), University of Illinois at Chicago, West Taylor Street 845Rm 2236, Chicago, 60607, Illinois, USA

    Ho-Ung Yee

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D’Hoker, E., Kraus, P. (2013). Quantum Criticality via Magnetic Branes. In: Kharzeev, D., Landsteiner, K., Schmitt, A., Yee, HU. (eds) Strongly Interacting Matter in Magnetic Fields. Lecture Notes in Physics, vol 871. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37305-3_18

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