Nonperturbative treatment of additional PMC terms in the broken-translation-invariance horizon condition

Determine whether the additional perfect magnetic conductor contributions generated by the broken-translation-invariance analysis of the no-pole condition become negligible in the infinite-volume limit relative to the leading four-dimensional bulk contribution.

Background

The paper analyzes the no-pole condition in the presence of parallel plates, where translation invariance is broken in the direction normal to the plates. The calculation is carried out explicitly only for perfect electric conductor boundaries; the perfect magnetic conductor case produces additional terms that are described as technically more difficult.

The authors argue that these extra PMC terms should become irrelevant in the infinite-volume limit because the boundary contributions carry lower-dimensional volume factors than the bulk terms. This expectation is not demonstrated and remains an unresolved part of the no-pole analysis.

References

Although this is open for further study, we expect that the extra PMC terms mentioned before become, in the infinite volume limit, obsolete as well when compared to the leading 4D bulk piece.

— The Casimir effect in Gribov-Zwanziger theory  (2609.11448 - Dudal et al., 10 Sep 2026) in Section 8, final paragraph of “No-pole condition for the ghost propagator with broken translation invariance”