Geometric Entropy and Hagedorn/Deconfinement Transition

TL;DR

This paper introduces geometric entropy as a new measure related to entanglement entropy, demonstrating its discontinuity at the Hagedorn temperature in super Yang-Mills theory and its gravity dual, indicating a phase transition.

Contribution

It proposes geometric entropy as a novel order parameter for confinement/deconfinement transitions and provides evidence of its discontinuity at the Hagedorn temperature.

Findings

Geometric entropy becomes discontinuous at the Hagedorn temperature.

Discontinuity observed in both free N=4 super Yang-Mills and supergravity dual.

Supports geometric entropy as an order parameter for phase transitions.

Abstract

It has recently been proposed that the entanglement entropy can be an order parameter of confinement/deconfinement transitions. To find a clear evidence, we introduce a new quantity called the geometric entropy, which is related to the entanglement entropy via a double Wick rotation. We analyze the geometric entropy and manifestly show that its value becomes discontinuous at the Hagedorn temperature both in the free N =4 super Yang-Mills and in its supergravity dual.