Entanglement temperature for the excitation of SYM theory in (De)confinement phase

TL;DR

This paper investigates the entanglement temperature in holographic supersymmetric Yang-Mills theory on hyperbolic space, revealing phase transition signatures even when Hawking temperature vanishes.

Contribution

It introduces a novel entanglement temperature applicable across all excitation parameters, providing insights into the dynamical and phase transition properties of excited SYM theory.

Findings

Entanglement temperature remains well-defined even when Hawking temperature disappears.

Signatures of phase transitions are identified through thermodynamic analysis.

The study links entanglement properties to dynamical phases of SYM theory.

Abstract

We study the holographic supersymmetric Yang-Mills (SYM) theory, which is living in a hyperbolic space, in terms of the entanglement entropy. The theory contains a parameter ($C$) corresponding to the excitation of the SYM theory, and it controls the dynamical properties of the theory. The entanglement temperature ($T_{ent}$) is obtained by imposing the thermodynamic law for the relative entanglement entropy and the energy density of the excitation. This temperature is available at any value of the parameter $C$ even in the region where the Hawking temperature disappears. With this new temperature, the dynamical properties of the excited SYM theory are examined in terms of the thermodynamic law. We could find the signatures of phase transitions of the theory.