Physical significance of central charges from singular transformations

Determine whether the central charges associated with the commutators of the physical boundary charges in the generalized Abelian gauge theory have a physically meaningful interpretation when non-singular central terms vanish and nonzero values require singular transformation parameters.

Background

The paper constructs boundary conditions for four-dimensional Abelian gauge theory coupled to general Chern–Simons boundary terms under which electric, magnetic, and boundary Chern–Simons combinations become physical conserved charges. Their Poisson brackets contain a possible central term proportional to an integral of dα∧dβ over the boundary of a spatial slice.

For non-singular transformation parameters, this central term vanishes. Nonzero values may arise for singular parameters, but the paper notes that such transformations can change the action and therefore do not define ordinary symmetry charges. The unresolved issue is whether the resulting central extensions nevertheless possess a physically meaningful interpretation.