Swampland SWSSB conjecture

Prove or disprove that, in any theory of quantum gravity admitting a weakly coupled Einstein-gravity description, with or without ensemble averages, every strong global symmetry of a mixed state is broken at least to a weak symmetry, so that the state exhibits either strong-to-weak spontaneous symmetry breaking or strong spontaneous symmetry breaking.

Background

The paper proposes extending the no-global-symmetry principle to strong symmetries of mixed states in quantum gravity. Because ensemble averages can produce weak emergent symmetries and because SWSSB provides a mixed-state realization of such emergence, the proposed conjecture requires strong global symmetries to be broken rather than remaining exact.

The conjecture is stated for theories with weakly coupled Einstein gravity, including descriptions involving ensemble averages. Its validity is not established; the paper specifically identifies string-theory compactifications as a setting in which it should be tested.