# More on Wilson loops for two touching circles

## TL;DR

This paper computes the renormalised Maldacena-Wilson loop for two touching circles with a cusp, analyzing weak and strong coupling regimes, especially as the cusp angle approaches zero, and compares it to a previous spiky case.

## Contribution

It provides the first detailed calculation of Wilson loops for touching circles with cusps at both weak and strong coupling, highlighting the behavior as the cusp angle vanishes.

## Key findings

- Behavior of Wilson loops as cusp angle approaches zero
- Comparison with previous spiky Wilson loop results
- Insights into cusp singularities at weak and strong coupling

## Abstract

We calculate both at leading weak and strong coupling the renormalised Maldacena-Wilson loop for contours formed by consecutive passage of two touching circles. At the touching point both circles should have the same normal direction but form cusps of non-zero opening angle $\alpha$. Particular emphasis is put on the behaviour in the limit $\alpha\rightarrow 0$ and its comparison with the spiky situation studied in a previous paper, where $\alpha$ was set to zero before renormalisation.