Measurement outcomes for the spherically symmetric 4D exotic wavefunction

Determine whether measurements of the spherically symmetric s-wave four-dimensional wavefunction—obtained by interpreting the two-dimensional transformed state as the s-wave component of four-dimensional fermions and attached to a volume defect between two spherical shells—yield spherically symmetric detection outcomes or angularly localized events; specify and analyze concrete measurement protocols to resolve this question and characterize how the answer depends on the measurement details.

Background

After constructing explicit two-dimensional wavefunctions for exotic excitations scattered by the Maldacena–Ludwig wall, the authors note that the same expressions can be used as the s-wave part of a four-dimensional fermionic scattering state. In this four-dimensional interpretation, the state is spherically symmetric and can be viewed as being attached to a volume defect between two spherical shells.

The authors explicitly raise the question of what a measurement would observe in such a state: whether detection outcomes remain spherically symmetric or become localized in angle. They acknowledge uncertainty and emphasize that a definitive answer requires specifying the measurement protocol, highlighting an unresolved problem at the interface of quantum measurement and the constructed scattering states.