  We consider the 4d compact U(1) theory with Wilson action and characterize
its phase diagram using the notion of electromagnetic flux, instead of the more
usual magnetic monopole. Taking inspiration from the flux picture, we consider
the helicity modulus (h.m.) for this theory, and show that it is an order
parameter for the confinement deconfinement phase transition. We extend the
definition of the h.m. to an Abelian projected Yang-Mills theory, and discuss
its behavior in SU(2).
