Reformulating the TBA equations for the quark anti-quark potential and their two loop expansion

Understand

The boundary thermodynamic Bethe Ansatz (BTBA) equations introduced in arXiv:1203.1913 and arXiv:1203.1617 to describe the cusp anomalous dimension contain imaginary chemical potentials and singular boundary fugacities, which make its systematic expansion problematic.

• We propose an alternative formulation based on real chemical potentials and additional source terms.
• We expand our equations to double wrapping order and find complete agreement with the direct two-loop gauge theory computation of the cusp anomalous dimension.