  The effective string theory emerging from the bilocal approximation to the
Method of Vacuum Correlators in gluodynamics is shown to be well described by
the 4D theory of the massive Abelian Kalb-Ramond field interacting with the
string, which is known to be the low-energy limit of the Universal Confining
String Theory. This correspondence follows from the agreement of the behaviour
of the coefficient functions, which parametrize the gauge-invariant correlator
of two gluonic field strength tensors, known from the lattice data, with their
values obtained from the propagator of the Kalb-Ramond field. We discuss this
correspondence in several aspects and demonstrate that the mass of the
Kalb-Ramond field in this approach plays the role of the inverse correlation
length of the vacuum, so that in the massless limit string picture disappears.
Next, we apply the background field method, known in the theory of nonlinear
sigma models, to obtain the action, which is quadratic in quantum fluctuations
around a given (e.g. minimal) string world-sheet. Several nontrivial types of
couplings of these fluctuations with the background world-sheet are obtained
and discussed.
