  Making use of the duality transformation, we derive in the Londons' limit of
the Abelian Higgs Model string representation for the 't Hooft loop average
defined on the string world-sheet, which yields the values of two coefficient
functions parametrizing the bilocal correlator of the dual field strength
tensors. The asymptotic behaviours of these functions agree with the ones
obtained within the Method of Vacuum Correlators in QCD in the lowest order of
perturbation theory. We demonstrate that the bilocal approximation to the
Method of Vacuum Correlators is an exact result in the Londons' limit, i.e. all
the higher cumulants in this limit vanish. We also show that at large
distances, apart from the integration over metrics, the obtained string
effective theory (which in this case reduces to the nonlinear massive axionic
sigma model) coincides with the low-energy limit of the dual version of 4D
compact QED, the so-called Universal Confining String Theory. We derive string
tension of the Nambu-Goto term and the coupling constant of the rigidity term
for the obtained string effective theory and demonstrate that the latter one is
always negative, which means the stability of strings, while the positiveness
of the former is confirmed by the present lattice data. These data enable us to
find the Higgs boson charge and the vacuum expectation value of the Higgs
field, which model QCD best of all. We also study dynamics of the weight factor
of the obtained string representation for the 't Hooft average in the loop
space. In conclusion, we obtain string representation for the partition
function of the correlators of an arbitrary number of Higgs currents, by virtue
of which we rederive the structure of the bilocal correlator of the dual field
strength tensors, which yields the surface term in the string effective action.
