Abstract
Motivated by the near-horizon geometry of four-dimensional extremal black holes, we study a disordered quantum mechanical system invariant under a global SU(2) symmetry. As in the Sachdev-Ye-Kitaev model, this system exhibits an approximate SL(2, ℝ) symmetry at low energies, but also allows for a continuous family of SU(2) breaking marginal deformations. Beyond a certain critical value for the marginal coupling, the model exhibits a quantum phase transition from the gapless phase to a gapped one and we calculate the critical exponents of this transition. We also show that charged, rotating extremal black holes exhibit a transition when the angular velocity of the horizon is tuned to a certain critical value. Where possible we draw parallels between the disordered quantum mechanics and charged, rotating black holes.
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Anninos, D., Anous, T. & D’Agnolo, R.T. Marginal deformations & rotating horizons. J. High Energ. Phys. 2017, 95 (2017). https://doi.org/10.1007/JHEP12(2017)095
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DOI: https://doi.org/10.1007/JHEP12(2017)095