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.
Highlights
Becomes that of a two-dimensional anti-de Sitter space, where the Killing symmetries are enhanced to those of the conformal group in (0 + 1)-dimensions: SL(2, R)
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
We show that charged, rotating extremal black holes exhibit a transition when the angular velocity of the horizon is tuned to a certain critical value
Summary
We review some of the thermodynamic features of the Kerr-Newman solution, stressing the role of the angular velocity of the horizon. This quantity has an analog in the quantum mechanics models described that controls the transition between different phases of the theory
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