Determine the complete dynamical deformation space of a five-dimensional fixture

Determine the precise form and number of independent dynamical deformations $\mathcal{F}'(y,z,u,v)$ of a five-dimensional SCFT fixture obtained by deforming a five-dimensional conformal-matter threefold, in order to compute its ultraviolet Higgs-branch dimension.

Background

The paper proposes a method for computing the ultraviolet Higgs-branch dimension of a five-dimensional fixture by counting deformations that remain available after a subset of the original conformal-matter deformations has been turned on.

It argues that the remaining deformations should be those that lower the Coulomb-branch rank, and verifies this proposal in one example. However, the general form of these deformations and a complete counting procedure are not established; the authors explicitly leave this determination unresolved and defer a comprehensive treatment.