The Area Term of the Entanglement Entropy of a Supersymmetric $O(N)$ Vector Model in Three Dimensions

TL;DR

This paper investigates the area term of entanglement entropy in a supersymmetric $O(N)$ model in 3D, revealing its independence from interaction couplings at criticality and exploring related fermionic Green's functions.

Contribution

It demonstrates the invariance of the entanglement entropy's area term along the critical line and introduces a novel mapping between fermionic Green's functions and the relativistic hydrogen atom.

Findings

Area term is coupling-independent at criticality

Proper counter terms are necessary for consistent limit evaluation

Fermionic Green's functions map to the relativistic hydrogen atom problem

Abstract

We studied the leading area term of the entanglement entropy of $\mathcal{N}=1$ supersymmetric $O(N)$ vector model in $2+1$ dimensions close to the line of second order phase transition in the large $N$ limit. We found that the area term is independent of the varying interaction coupling along the critical line, unlike what is expected in a perturbative theory. Along the way, we studied non-commuting limits $n-1\to 0$ verses UV cutoff $r\to 0$ when evaluating the gap equation and found a match only when appropriate counter term is introduced and whose coupling is chosen to take its fixed point value. As a bonus, we also studied Fermionic Green's functions in the conical background. We made the observation of a map between the problem and the relativistic hydrogen atom.