U(1) Holonomy Algebra on Null Initial Surfaces
Carolina Sole Panella (Erlangen-Nürnberg U.)
Abstract: We study the quantisation of Wilson line operators on null surfaces using the Maxwell field as a simplified framework. Unlike the spacelike case, electric and magnetic fluxes on a null surface are not independent, causing holonomies to no longer commute. Regularising paths as thin ribbons, we find that Wilson lines commute unless they share a light ray, with structure constants depending on the intersection geometry and the conformal class of the null metric. Upon quantisation, holonomies become Grassmann-valued, pairs of Wilson lines can interpolate continuously between fermionic and bosonic statistics, and the ground state depends on a framing choice of the underlying paths.