Spin-Refined Partition Functions and $\mathcal{CRT}$ Black Holes

TL;DR

This paper explores spin-refined partition functions in AdS/CFT, revealing phase structures and dominant black hole contributions, especially under $ ext{CRT}$ symmetry, and discusses ensemble differences in microcanonical settings.

Contribution

It introduces the concept of spin-refined partition functions in AdS/CFT, analyzes their phase diagrams, and identifies $ ext{CRT}$-twisted black holes as dominant at high temperature.

Findings

High-temperature regimes are dominated by $ ext{CRT}$-twisted black holes.

In odd dimensions, complex rotating black holes may influence spin-refined observables.

Microcanonical ensemble analysis shows rotating black holes often dominate, indicating ensemble inequivalence.

Abstract

We investigate spin-refined partition functions in AdS/CFT using Euclidean gravitational path integrals. We construct phase diagrams for $Z_X = \text{Tr} \big( e^{-\beta H} X \big)$ in various dimensions and for different choices of discrete isometry $X$, discovering rich structures at finite temperature. When $X$ is a reflection, $Z_X$ counts the difference between the number of even- and odd-spin microstates. The high-temperature regime is universally dominated by $\mathcal{CRT}$-twisted black holes in any dimension, and in odd spacetime dimensions we examine whether complex rotating black hole solutions can contribute to spin-refined observables or potentially dominate at finite temperature. We also analyze the microcanonical ensemble. There the leading contribution almost always comes from rotating black holes, showing that the two ensembles are not necessarily equivalent.