Establish the correct higher-dimensional tunneling contribution

Determine whether the tunneling solution used to compute the dominant three-dimensional axion necklace contribution is also the correct quantum-mechanical contribution in higher-dimensional axion wormhole models.

Background

The higher-dimensional analysis relies on semiclassical and numerical evidence rather than an exact quantum propagator. The authors compute a pole contribution associated with the tunneling trajectory and compare it with the necklace action.

Only in three dimensions do they establish from the exact quantum mechanics that the tunneling solution governs the propagator. In higher dimensions, the assumed tunneling contribution could yield an entropy exceeding the de Sitter entropy and hence violate the second law. Determining whether the tunneling trajectory is genuinely selected by the higher-dimensional quantum theory would resolve this issue.