Abstract
We present the generating function approach to the perturbative exponentiation of correlators of a product of Wilson lines and loops. The exponentiated expression is presented in closed form as an algebraic function of correlators of known operators, which can be seen as a generating function for web diagrams. The expression is naturally split onto two parts: the exponentiation kernel, which accumulates all non-trivial information about web diagrams, and the defect of exponentiation, which reconstructs the matrix exponent and is a function of the exponentiation kernel. The detailed comparison of the presented approach with existing approaches to exponentiation is presented as well. We also give examples of calculations within the generating function exponentiation, namely, we consider different configurations of light-like Wilson lines in the multi-gluon-exchange-webs (MGEW) approximation. Within this approximation the corresponding correlators can be calculated exactly at any order of perturbative expansion by only algebraic manipulations. The MGEW approximation shows violation of the dipole formula for infrared singularities at three-loop order.
Highlights
The exponentiation property for Abelian gauge theories has been understood a long time ago [1]
We present the generating function approach to the perturbative exponentiation of correlators of a product of Wilson lines and loops
The exponentiated expression is presented in closed form as an algebraic function of correlators of known operators, which can be seen as a generating function for web diagrams
Summary
In the paper we present an exponentiation method for a product of Wilson lines and compare it with other exponentiation approaches presented in literature. In the consequence of the expression (2.2) only the two-Wilson-lines-irreducible diagrams have non-zero modified color factors These diagrams form the set of webs for the cusp, or for the Wilson loop. The web-mixing matrix should be calculated at every order of the perturbative expression independently, what makes any general consideration difficult In this aspect, the replica exponentiation resembles the diagrammatic exponentiation for the product of Wilson lines [7] The main distinctive feature of the approach is the presentation of the exponentiated series in closed form, namely, as a function of correlators of known operators This function can be interpreted as a generating function for web diagrams [9]. In contrast to the diagrammatic and the replica exponentiations, the GF exponentiation has a visual and simple expression
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call