Marginal deformations & 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, 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.

Gravitational anomalies in nAdS2/nCFT1

“…And so the persistent trend in nAdS 2 holography, coined with a 'n' since we are 'near' to our original configuration, is that the deviations away from extremality are controlled by this pattern. For a review see [14].The application of this new framework to black hole physics has shown that, while JT models capture common features [15][16][17][18][19][20], the additional parameters for more general black holes display interactions that are not present in JT gravity [21][22][23][24][25][26][27]. This makes clear that there is new phenomena to be explored, that simpler models do not take into account.Our interest therefore is to further explore the properties of nAdS 2 /nCFT 1 with the goal of building a more refined understanding of the dynamics near the horizon of (near-)extremal black holes.…”

Charged quantum fields in AdS$_2$

“…We also see now that the kernel in (2.24) is indeed a conformal two-point function of two complex operators in the principal series with weight λ = 1/2 + is, such that (2.24) can be viewed as a type of shadow transform. We will see examples of both types of correlators in section 5 and appendix B. Correlators for λ = λ ′ = 1/2 containing both terms in (2.28) where found in [9]. One could also have derived these correlators by staying in position space and using the following differential operator representation of the sl(2, R) generators,…”

“…The symmetries of the system are now SL(2, R) × U (1). Explicitly we have: 9) and α ζ 0 = 0. The general solution for the flat strip is given by…”

“…Here, we discuss the construction of a state in the |Υ Hilbert space that approximates |Ω . Define the following 9) with N being some large positive integer. We note that,…”

“…However, most efforts have so far focused on the case with a two-dimensional bulk rather than the more realistic four-dimensional solutions of general relativity containing an AdS 2 factor. Part of the motivation for this work is to understand whether the lessons learned from the recent holographic models of AdS 2 holography can be applied to the extreme Kerr geometry [9]. 1 There are several features that make this both interesting as well as challenging.…”