Universal Terms of Entanglement Entropy for 6d CFTs

TL;DR

The paper tackles the universal logarithmic terms of entanglement entropy for six-dimensional conformal field theories, deriving them through both holographic and field-theoretical perspectives. By employing a holographic setup with higher-curvature gravity and a field-theoretic Weyl anomaly approach, it isolates the conformal invariants that contribute to EE, denoted as $F_1$, $F_2$, and $F_3$, alongside the Euler density $E_4$. A central result is the exact agreement between holographic and field-theory calculations for the $C^2$ and $Ck^2$ terms, while the $k^4$ terms require a careful splitting of conical metrics (the splitting problem); this splitting is fixed in the bulk by equations of motion and constrained on the boundary to ensure consistency, with partial boundary freedom not affecting the universal EE. The work also shows that, under suitable central-charge relations, certain combinations of the $F_i$ invariants are boundary-splitting independent, underscoring the robustness of the universal structure and contributing to resolving historic HMS mismatches by incorporating anomaly-like contributions. Altogether, the results advance a conformally invariant, cross-validated framework for universal EE in 6d CFTs and clarify how holographic and field-theoretic data encode higher-dimensional conformal structure.

Abstract

We derive the universal terms of entanglement entropy for 6d CFTs by applying the holographic and the field theoretical approaches, respectively. Our formulas are conformal invariant and agree with the results of [34,35]. Remarkably, we find that the holographic and the field theoretical results match exactly for the $C^2$ and $Ck^2$ terms. Here $C$ and $k$ denote the Weyl tensor and the extrinsic curvature, respectively. As for the $k^4$ terms, we meet the splitting problem of the conical metrics. The splitting problem in the bulk can be fixed by equations of motion. As for the splitting on the boundary, we assume the general forms and find that there indeed exists suitable splitting which can make the holographic and the field theoretical $k^4$ terms match. Since we have much more equations than the free parameters, the match for $k^4$ terms is non-trivial.