Inverted c-functions in thermal states

TL;DR

This paper investigates how entanglement entropy and holographic c-functions behave in thermal states of strongly coupled  Super-Yang-Mills theory, revealing an inverted c-theorem and the influence of chiral anomalies and magnetic fields.

Contribution

It demonstrates an inverted c-theorem for holographic c-functions in thermal states, contrasting with vacuum states, and explores anomaly and magnetic field effects on these functions.

Findings

Holographic c-functions increase towards the IR in thermal states.

In the IR limit, c-functions grow proportionally to thermal entropy.

Chiral anomaly effects peak at intermediate magnetic fields.

Abstract

We first compute the effect of a chiral anomaly, charge, and a magnetic field on the entanglement entropy in $\mathcal{N}=4$ Super-Yang-Mills theory at strong coupling via holography. Depending on the width of the entanglement strip the entanglement entropy probes energy scales from the ultraviolet to the infrared energy regime of this quantum field theory (QFT) prepared in a given state. From the entanglement entropy, we compute holographic c-functions and demonstrate an inverted c-theorem for them. That is, these c-functions in generic thermal states monotonically increase towards the infrared (IR) energy regime. This is in contrast to the c-functions in vacuum states which decrease along the renormalization group flow towards the IR regime of a renormalizable QFT. Furthermore, in thermal states and in the IR limit, the c-functions behave thermally, growing proportionally to the value of the thermal entropy. The chiral anomaly affects the c-functions more in the IR regime, and its effect is peaked at an intermediate value of the magnetic field at a fixed chemical potential and temperature.