Marginal Deformations and Rotating Horizons

TL;DR

This paper investigates a disordered quantum system inspired by extremal black holes, revealing a phase transition influenced by marginal deformations and drawing parallels with rotating black hole horizons.

Contribution

It introduces a model with $SU(2)$ symmetry and marginal deformations, analyzing its phase transition and connecting it to black hole horizon phenomena.

Findings

Identifies a quantum phase transition at a critical marginal coupling.

Calculates critical exponents for the phase transition.

Draws parallels between quantum mechanics and black hole horizon behavior.

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.