Strong-coupling expansion of cusp anomaly from quantum superstring

Understand

We consider the world surface in AdS_5 that ends on two intersecting null lines at the boundary.

• The corresponding string partition function describes the expectation value of the Wilson line with a null cusp in dual large N maximally supersymmetric gauge theory and thus determines the cusp anomaly function f(\lambda) of the gauge coupling.
• The first two coefficients in its strong-coupling or string inverse tension expansion were determined in hep-th/0210115 (a_1=1) and in arXiv:0707.4254 (a_2=- 3 log 2).
• Here we find that the 2-loop coefficient is a_2 = - K where K is the Catalan's constant.