Marginal Deformations and Rotating Horizons

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 $SL(2,\mathbb{R})$ 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.

29 pages, 5 figures

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Cited by in corpus (22)

• The statistical mechanics of near-extremal black holes
• 5D Rotating Black Holes and the nAdS${}_2$/nCFT${}_1$ Correspondence
• Jackiw-Teitelboim Gravity and Rotating Black Holes
• A note on the complex SYK model and warped CFTs
• Constructing AdS_2 flow geometries
• Supersymmetric SYK Model with Global Symmetry
• Breaking away from the near horizon of extreme Kerr
• Logarithmic Corrections to Black Hole Entropy: the Non-BPS Branch
• Charged Quantum Fields in AdS${}_2$
• Gravitational perturbations from NHEK to Kerr
• Rotating 5D Black Holes: Interactions and deformations near extremality
• Phases of $\mathcal{N}=2$ Sachdev-Ye-Kitaev models
• From black holes to baby universes in CGHS gravity
• An invitation to the principal series
• Jackiw-Teitelboim Model Coupled to Conformal Matter in the Semi-Classical Limit
• Gravitational Anomalies in nAdS${}_2$/nCFT${}_1$
• Pair Production of Scalar Dyons in Kerr-Newman Black Holes
• Note on global symmetry and SYK model
• Warped Flatland
• How to Build a Black Hole out of Instantons
• Statistical Mechanics of Exponentially Many Low Lying States
• The quantum $p$-spin glass model: A user manual for holographers