Quantum corrected black hole microstates and entropy

TL;DR

This work extends the microscopic accounting of black hole entropy to include quantum corrections using a doubly holographic construction with a JT brane and holographic matter coupled to two CFTs. By computing a quantum-corrected partition function and generalized entropy, the authors show that the microstate count is exp(S_micro) with S_micro equal to the sum of quantum-corrected thermodynamic entropies of the two horizons, and that this quantity coincides with the generalized entropy S_gen of the eternal black hole, encoding inter-boundary entanglement. The analysis uses bulk/brane/boundary dual pictures to derive the quantum corrections, perform microstate construction with shells, and perform Gram-matrix based state counting to reproduce the corrected entropy. The results connect microscopic degeneracy to inter-boundary entanglement and provide a framework for including O(G_N^0) corrections in doubly holographic black holes, with potential extensions to higher dimensions and more general matter content.

Abstract

We extend the semiclassical black hole microstate construction to include quantum corrections to the microscopic entropy using a doubly holographic model of black holes. Specifically, we consider a double-sided black hole on a JT brane with holographic matter, coupled to a pair of holographic CFTs on the asymptotic boundaries. The dimension of the Hilbert space spanned by the microstates of this doubly holographic black hole is given by the exponentiated entropy, which is equal to the sum of the quantum-corrected thermodynamic entropies of the left and right black holes. Importantly, the quantum-corrected thermodynamic entropy is shown to be equal to the generalised entropy of the eternal black hole, and thus can be interpreted as quantifying the entanglement between the two asymptotic boundaries.

Figures (7)

• Figure 1: The gluing of two copies of the BTZ solution along the brane (purple) in a $Z_2$ symmetric way.
• Figure 2: A constant time slice of the Euclidean semiclassical geometry in \ref{['fig:geombulk']} with the brane in purple. The subregion $\mathbf{R}$ is taken to be one of the two boundaries visualised in green. The candidate extremal surfaces $\Sigma'_\mathbf{R}$ are indicated in grey and intersect the brane at $\sigma'_\mathbf{R}$. The minimal surface $\Sigma_\mathbf{R}$ given in red coincides with the horizon and intersects the brane at $\sigma_\mathbf{R}$.
• Figure 3: The Euclidean path integral that prepares the state given in \ref{['eq: state-CFT-gen']}. The spherically symmetric shell is denoted by the red circle, which intersects with the conformal defect at $\phi=0$ denoted by the purple line.
• Figure 4: A constant time slice of the Euclidean semiclassical geometry dual to the state given by \ref{['eq: state-CFT-gen']}. The thin shell of matter dual to the operator $\mathcal{O}^{(k)}$ is denoted by red, and the brane connecting the two asymptotic boundaries is denoted by purple. Left: the bulk geometry is cut by the shells and branes, and the identification for the glueing. Right: the geometry after the glueing.
• Figure 5: The 3d Euclidean semiclassical geometry dual to the state given by \ref{['eq: state-CFT-gen']}. The brane $\mathcal{B}$ is denoted by the purple region, and the thin shell is denoted by the red region. The brane trajectory is given by \ref{['eq: brane-equation']} and the shell trajectory is given by \ref{['eq: trajectory-shell']}.