Higher entanglement cohomology classes in the bulk

Characterize the bulk interpretation of the higher entanglement cohomology classes H^n_ent for n ≥ 2.

Background

The paper tests the proposed holographic correspondence between a distinguished subspace of the first entanglement cohomology group H1_ent and linearized modular Hamiltonian perturbations of the bulk entanglement wedge. After verifying the correspondence for d = 2, 3, and 4, it identifies the interpretation of higher cohomology classes as an unresolved direction extending beyond the first cohomology class.

References

The interpretation of higher cohomology classes $Hn_{\mathrm{ent}$ ($n \geq 2$) in the bulk remains open.

— Higher-Dimensional Test of the Holographic Dual of Entanglement Cohomology  (2610.25969 - ~Rashkov, 19 Oct 2026) in Section 5, subsection “Check of the general-d coefficient”

The natural conjecture is that the map $[\Phi_{uE}] \mapsto \delta K_A$ persists with $\delta K_A$ computed from the deformed modular Hamiltonian. A quantitative check for backgrounds such as the $\beta$-deformed AdS$_5 \times S5$ or the $T\bar{T}$-deformed AdS$_3$ is left for future work.

— Higher-Dimensional Test of the Holographic Dual of Entanglement Cohomology  (2610.25969 - ~Rashkov, 19 Oct 2026) in Section 5, subsection “Outlook: TsT-Deformed Backgrounds”