EFT consistency of KKLT-like vacua under vacuum superposition induced by thick domain walls

Ascertain to what extent the presence of small potential barriers and thick domain walls—implying that the ground-state wavefunction is a superposition over vacua with different flux numbers—affects the consistency of constructing a four-dimensional effective field theory around a single classical KKLT-like vacuum.

Background

If KKLT minima are taken as consistent, the presence of small barriers and thick domain walls suggests that the ground state is not localized in a single classical vacuum but rather spreads over vacua distinguished by flux quantum numbers, analogous to the θ-vacuum in QCD.

Since EFTs are typically formulated around a single classical vacuum with small fluctuations, the authors note that it is unclear to what extent this superposition picture undermines the consistency of the KKLT-like EFT construction.

References

Here this picture seems altered, and it is not clear to us to what extent this affects the consistency of the construction of KKLT-like vacua we have discussed.

— A domain wall bound on anti-de Sitter vacua  (2603.08779 - Cribiori et al., 9 Mar 2026) in Conclusions (middle paragraph)

Whether this class-group action can be promoted to a physical symmetry of a single four-dimensional effective theory requires further investigation.

— Note on arithmetic structure of modulus vacua in flux compactifications  (2608.24054 - Furuta et al., 25 Aug 2026) in Section 6, Conclusions