Observations on entanglement entropy in massive QFT's

TL;DR

The paper analyzes universal contributions to entanglement entropy in massive quantum field theories using curved waveguide geometries and holographic methods. It derives Rényi-entropy results for free massive scalars and fermions via heat kernels and $\zeta$-function regularization, uncovering curvature-driven universal terms on the entangling surface, including a Ricci-scalar contribution with coefficients that depend on the curvature coupling $\xi$ and on fermionic or scalar content. It then performs a strong-coupling holographic calculation for ${\cal N}=2^*$, finding a universal logarithmic term proportional to $m_f^2 \log(m_f\delta)$ that depends only on the fermionic mass, with bosonic masses not contributing to this coefficient, and a notable factor-of-three mismatch with the weak-coupling result in the fermionic sector. Together these results illuminate the geometric structure of entanglement entropy in QFT, test holographic predictions, and point to subtle coupling-dependent effects that merit further study across dimensions and holographic RG flows.

Abstract

We identify various universal contributions to the entanglement entropy for massive free fields. As well as the `area' terms found in [1], we find other geometric contributions of the form discussed in [2]. We also compute analogous contributions for a strongly coupled field theory using the AdS/CFT correspondence. In this case, we find the results for strong and weak coupling do not agree.