# Large-size expansion for triangular Wilson loops in confining gauge theories

## TL;DR

This paper derives a simple expression for the large-size expansion of triangular Wilson loops in confining gauge theories, revealing the two-loop correction within effective string theory and addressing ultraviolet divergences.

## Contribution

It introduces an analytical regularization method for two-loop corrections in Wilson loops, providing explicit results for triangular contours in confining gauge theories.

## Key findings

- Derived a simple formula for the $L^{-2}$ term in triangular Wilson loops.
- Renormalized ultraviolet divergences using Schwarz-Christoffel mapping.
- Connected two-loop corrections to effective string theory in confining gauge theories.

## Abstract

The asymptotic behavior of Wilson loops in the large-size limit ($L\rightarrow\infty$) in confining gauge theories with area law is controlled by effective string theory (EST). The $L^{-2}$ term of the large-size expansion for the logarithm of Wilson loop appears within EST as a two-loop correction. Ultraviolet divergences of this two-loop correction for polygonal contours can be renormalized using an analytical regularization constructed in terms of Schwarz-Christoffel mapping. In the case of triangular Wilson loops this method leads to a simple final expression for the $L^{-2}$ term.