Determine the appropriate microscopic treatment of non-Regge area-metric modes

Determine whether imposing strong geometric closure is the appropriate microscopic modification of spinfoam dynamics, or whether the additional area-metric, non-length degrees of freedom should instead be retained and controlled dynamically or through renormalization.

Background

The paper relates its geometric-closure proposal to continuum-limit analyses in which spinfoam dynamics contains additional non-length degrees of freedom, described in terms of area-metric or non-metric modes. Strong geometric closure removes the non-closed directions locally and restricts the semiclassical configuration space to length-Regge geometries.

The authors emphasize that it remains unresolved whether this strong restriction is physically appropriate at the microscopic level. An alternative is to retain the additional area-metric modes and control them dynamically or by means of renormalization. This question concerns the correct microscopic theory underlying the semiclassical spinfoam description.