Fluctuating Strings in the Universal Confining String Theory and Gluodynamics

TL;DR

This paper demonstrates that the effective string theory in gluodynamics aligns with a 4D massive Abelian Kalb-Ramond field framework, linking lattice data with low-energy confining string descriptions and exploring fluctuation couplings.

Contribution

It establishes a correspondence between the effective string theory from gluodynamics and the Kalb-Ramond field approach, revealing the role of mass as the inverse correlation length.

Findings

Agreement of gauge-invariant correlator functions with Kalb-Ramond propagator

Mass of the Kalb-Ramond field corresponds to vacuum correlation length

Derived quadratic action for quantum fluctuations around string world-sheet

Abstract

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.