Pair Correlation Function of Wilson Loops

TL;DR

This paper develops a path integral method to compute the pair correlation function of Wilson loops in string theory, revealing universal short-distance interactions and velocity-dependent corrections in gauge theories.

Contribution

It introduces a novel prescription for calculating Wilson loop correlations in bosonic string theory applicable in flat or curved backgrounds, and analyzes the resulting potential between sources.

Findings

Universal -(d-2)/r static interaction at short distances

Velocity corrections form an infinite power series in dimensionless variables

Potential behavior analyzed in both flat and curved backgrounds

Abstract

We give a path integral prescription for the pair correlation function of Wilson loops lying in the worldvolume of Dbranes in the bosonic open and closed string theory. The results can be applied both in ordinary flat spacetime in the critical dimension d or in the presence of a generic background for the Liouville field. We compute the potential between heavy nonrelativistic sources in an abelian gauge theory in relative collinear motion with velocity v = tanh(u), probing length scales down to r_min^2 = 2 \pi \alpha' u. We predict a universal -(d-2)/r static interaction at short distances. We show that the velocity dependent corrections to the short distance potential in the bosonic string take the form of an infinite power series in the dimensionless variables z = r_min^2/r^2, uz/\pi, and u^2.