An 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 behavior 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 worldsheet. Several nontrivial types of couplings of these fluctuations with the background worldsheet are obtained and discussed.
Background field method for nonlinear sigma models in nonrelativistic string theory
