Analytical renormalization of large-size expansion for polygonal Wilson loops in effective string theory

TL;DR

This paper proves that a new analytical regularization method based on Schwarz-Christoffel mapping yields finite, consistent results for large-size expansions of polygonal Wilson loops in effective string theory, regardless of the specific SC mapping used.

Contribution

It demonstrates the general applicability and independence of the analytical renormalization method for arbitrary polygonal Wilson loops in effective string theory.

Findings

The regularization produces finite results for any polygonal Wilson loop.

Results are independent of the choice of Schwarz-Christoffel mapping.

The method extends previous two-loop calculations to arbitrary polygons.

Abstract

Schwarz-Christoffel (SC) mapping plays a crucial role in the calculation of the large-size expansion for polygonal Wilson loops in confining gauge theories using effective string theory (EST). Recently a new analytical regularization based on SC mapping was suggested and successfully applied to the calculation of the two-loop contribution of EST in the case of triangular Wilson loops. We prove that this analytical renormalization produces finite results for arbitrary polygonal Wilson loops and show that the result of the analytical renormalization for a given polygonal contour is independent of the choice of SC mapping for this polygon.