Exploring the mirror TBA

Understand

We apply the contour deformation trick to the Thermodynamic Bethe Ansatz equations for the AdS_5 \times S^5 mirror model, and obtain the integral equations determining the energy of two-particle excited states dual to N=4 SYM operators from the sl(2) sector.

• We show that each state/operator is described by its own set of TBA equations.
• Moreover, we provide evidence that for each state there are infinitely-many critical values of 't Hooft coupling constant \lambda, and the excited states integral equations have to be modified each time one crosses one of those.
• In particular, estimation based on the large L asymptotic solution gives \lambda \approx 774 for the first critical value corresponding to the Konishi operator.