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

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 $s_{\text{EE}}^d$ 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 $d=3+4n$.

Entanglement Entropy, Conformal Field Theory, Fractional Interactions

References in corpus (5)

• Towards a derivation of holographic entanglement entropy
• Holographic c-theorems in arbitrary dimensions
• Entanglement entropy across a deformed sphere
• Some results on the shape dependence of entanglement and Rényi entropies
• Three dimensional Yukawa models and CFTs at strong and weak couplings

Cited by in corpus (1)

• Determining all thermodynamic transport coefficients for an interacting large N quantum field theory