Interacting CFTs for all couplings: Thermal versus Entanglement Entropy at Large $N$

TL;DR

This paper constructs a new class of interacting conformal field theories in odd dimensions and analyzes their thermal and entanglement entropies across all couplings, revealing constant entanglement entropy and specific thermal entropy ratios.

Contribution

It introduces a novel large N limit approach for marginal O(N) models with non-polynomial potentials in odd dimensions, providing explicit calculations of thermal and entanglement entropies for all couplings.

Findings

Vacuum entanglement entropy is constant for all couplings in odd dimensions.

Thermal entropy ratio in 2+1 dimensions matches recent results (4/5).

Thermal entropy decreases monotonically with coupling in odd dimensions.

Abstract

In this paper, I calculate the large $N$ limit of marginal $O(N)$ models with non-polynomial potentials in arbitrary odd dimensions $d$. This results in a new class of interacting pure conformal field theories (CFTs) in $d=3+4n$ for any $n \in \mathbb{Z}_+$. Similarly, in $d=3+4n$ I calculate the thermal entropy for all couplings on $R^{2+4n} \times S^1$ for $n=0,1,2,3$. In 2+1 dimensions I find the strong-to-weak coupling ratio of the thermal entropy to be 4/5, matching recent results, and further extend this analysis to higher odd dimensions. Next, I calculated the vacuum entanglement entropy $s^d_{\text{EE}}$ on $S^{d-2}$ for all couplings in arbitrary odd $d$ in the large N limit. I find the vacuum entanglement entropy on $S^{d-2}$ to be not only solvable but also constant for all couplings $\lambda$. Thus, in the large $N$ limit, the vacuum entanglement entropy on $S^{d-2}$ for odd $d$ is constant for all $\lambda$, in contrast to the thermal entropy which is shown to also be monotonically decreasing with $\lambda$ in $d=3+4n$.