Conformal Symmetry Breaking and Thermodynamics of Near-Extremal Black Holes

TL;DR

The paper demonstrates that the scale at which conformal symmetry in the near-horizon AdS$_2$ region of near-extremal black holes breaks due to backreaction, denoted $E_{br}$, is identical to the thermodynamic mass gap $M_{gap}$ obtained from low-temperature thermodynamics. Using both a bulk linearized quantum field theory approach and the universal Jackiw-Teitelboim (JT) model, it shows $E_{br}$ and $M_{gap}$ scale with the same IR data across extremal BTZ, spherical AdS RN, and planar AdS black holes, establishing a general equality $E_{br} \sim M_{gap}$. The JT model emerges as a universal IR description, enabling a robust link between dynamical backreaction effects and thermodynamic constraints in a wide class of near-extremal black holes. These results strengthen the AdS$_2$/CFT$_1$ intuition and highlight a deep connection between infrared conformal breaking and the finite-temperature thermodynamics of black holes, while opening questions about quantum corrections and extensions to Kerr geometries.

Abstract

It has been argued recently by Almheiri and Polchinski that the near-horizon conformal symmetry of extremal black holes must be broken due to gravitational backreaction at an IR scale linear in $G_N$. In this paper, we show that this scale coincides with the so-called `thermodynamic mass gap' of near-extremal black holes, a scale which signals the breakdown of their thermodynamic description. We also develop a method which extends the analysis of Almheiri and Polchinski to more complicated models with extremal throats by studying the bulk linearized quantum field theory. Moreover, we show how their original model correctly captures the universal physics of the near-horizon region of near-extremal black holes at tree level, and conclude that this equivalence of the conformal breaking and mass gap scale is general.