Holographic Entanglement Entropy in Static Patch Holography (Constrained Extremization)
Develop and justify a constrained extremization prescription for holographic entanglement entropy in de Sitter static patch holography by proving that S(A)=min_ext_{D_I} Σ_I Area(γ_I)/(4G)+O(G^0) with γ_I constrained to lie in region D_I and be D_I-homologous to A, ensuring consistency with entropy inequalities and entanglement wedge properties.
References
Conjecture [Holographic entanglement entropy in static patch holography] Let $A$ be a subsystem of $\Sigma\vert_{\mathcal{S}{\rm L}\cup\Sigma\vert{\mathcal{S}{\rm R}$. The entanglement entropy of $A$ is given by \begin{equation} \label{eq:FPRT} S(A)= \min \mathrm{ext}{D_I}\left[\sum_{I=L,E,R}\frac{\rm Area}(\gamma_I)}{4G}\right] +O(G0), \end{equation} where $\gamma_I$ must be $D_I$-homologous to $A$, and $\mathrm{ext}_{D_I}$ corresponds to a constrained extremization in $D_I$.