Dice Question Streamline Icon: https://streamlinehq.com

Generalize refined BBPSV operators to commute with all asymptotic charges

Develop the full generalization of the refined BBPSV operator construction so that, beyond commuting with the Hamiltonian, the resulting operators commute with all asymptotic symmetry generators by integrating over the asymptotic symmetry group and specifying the necessary measures and implementation details.

Information Square Streamline Icon: https://streamlinehq.com

Background

The refined BBPSV construction produces operators that commute with the Hamiltonian while reproducing the leading-order action of local bulk operators on a code subspace. The authors argue that, provided the background breaks all symmetries, the same idea should extend to all asymptotic charges by integrating over the full asymptotic symmetry group.

They outline the approach but explicitly leave the technical details to future work.

References

This can be achieved by replacing the integral in $T$ with an integral over the asymptotic symmetry group (SO(2,d) in our AdS case) with an appropriate measure, and $e{\pm iTH}$ with $U(g)$. We leave the details of this generalisation to future work.

— An apologia for islands (2506.04311 - Antonini et al., 4 Jun 2025) in Section 5.2 (Refined BBPSV operators)