Dynamics of the Universal Confining String Theory on the Loop Space

TL;DR

This paper develops a new loop equation for the Wilson average in 4D compact QED, revealing the dynamics of the confining string and deriving a solvable integral equation for the Wilson loop.

Contribution

It introduces an alternative loop equation decoupling transverse and longitudinal dynamics and derives a linear integral equation for the Wilson loop in coordinate space.

Findings

Decoupling of transverse and longitudinal components in the loop equation

Identification of a critical momentum discontinuity where transverse propagation ceases

Derivation of a linear integral equation for Wilson loops in coordinate space

Abstract

Starting with the representation of the Wilson average in the Euclidean 4D compact QED as a partition function of the Universal Confining String Theory, we derive for it the corresponding loop equation, alternative to the familiar one. In the functional momentum representation the obtained equation decouples into two independent ones, which describe the dynamics of the transverse and longitudinal components of the area derivative of the Wilson loop. At some critical value of the momentum discontinuity, which can be determined from a certain equation, the transverse component does not propagate. Next, we derive the equation for the momentum Wilson loop, where on the left-hand side stands the sum of the squares of the momentum discontinuities, multiplied by the loop, which describes its free propagation, while the right-hand side describes the interaction of the loop with the functional vorticity tensor current. Finally, using the method of inversion of the functional Laplacian, we obtain for the Wilson loop in the coordinate representation a simple Volterra type-II linear integral equation, which can be treated perturbatively.