Abstract
Four dimensional gravity with a U(1) gauge field, coupled to various fields in asymptotically anti-de Sitter spacetime, provides a rich arena for the holographic study of the strongly coupled (2+1)-dimensional dynamics of finite density matter charged under a global U(1). As a first step in furthering the study of the properties of fractionalized and partially fractionalized degrees of freedom in the strongly coupled theory, we construct electron star solutions at zero temperature in the presence of a background magnetic field. We work in Einstein–Maxwell-dilaton theory. In all cases we construct, the magnetic source is cloaked by an event horizon. A key ingredient of our solutions is our observation that starting with the standard Landau level structure for the density of states, the electron star limits reduce the charge density and energy density to that of the free fermion result. Using this result we construct three types of solution: One has a star in the infra-red with an electrically neutral horizon, another has a star that begins at an electrically charged event horizon, and another has the star begin a finite distance from an electrically charged horizon.
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Notes
- 1.
The idea that these holographic systems may capture the dynamics of fractionalized phases seems to have first begun to emerge in the work of Ref. [23] in their semi-holographic approach to the low energy physics. There, they used the term “quasiunparticle” for the effective particles in the unfractionalized phase. In work dedicated to addressing the issue, Ref. [24] further elucidated the connection between holographic physics and fractionalized phases. See Refs. [9, 10] for a review of some of these ideas.
- 2.
We emphasize that our work is both qualitatively and quantitatively different from Ref. [34]. Their work is in five dimensions, for a spherical star, and their TOV treatment involves an electrically neutral star.
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Acknowledgements
TA, CVJ, and SM would like to thank the US Department of Energy for support under grant DE-FG03-84ER-40168. TA is also supported by the USC Dornsife College of Letters, Arts and Sciences. We thank Kristan Jensen, Joe Polchinski, and Herman Verlinde for comments.
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Albash, T., Johnson, C.V., McDonald, S. (2013). Holography, Fractionalization and Magnetic Fields. 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_20
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