Conjecture on Higgs branch Schur operators under KK reduction

Let a four-dimensional superconformal field theory be reduced on a Kaluza–Klein circle, and consider its Schur operators. The scalar Schur operators are the Higgs branch operators.

Higgs-branch survival conjecture. The vector space of Higgs branch Schur operators is not affected by the KK reduction.

This is property A in the paper's discussion of the fate of scalar Schur operators. The authors describe it as a natural expectation motivated by the standard lore that the Higgs branch is unaffected by KK reduction, while noting that a general argument establishing it is not provided.