Holonomy operator for spin connection in twisted geometry

In this article we construct the holonomy operator for spin connection in (1+3)-dimensional LQG based on the twisted geometry. The starting point of the construction is to express the holonomy of the spin connection on a graph in terms of the twisted geometry variables, and we check that this expression reproduces the spin connection in terms of triads in a certain continuum limit. By using the twisted geometry parametrization of the holonomy-flux phase space, we further express the holonomy of the spin connection in terms of fluxes. Finally, it is promoted as well-defined operators by replacing the fluxes with ordered flux operators.