Thermodynamic bubble ansatz

Motivated by the computation of scattering amplitudes at strong coupling, we consider minimal area surfaces in AdS5 which end on a null polygonal contour at the boundary. We map the classical problem of finding the surface into an SU(4) Hitchin system. The polygon with six edges is the first non-trivial example. For this case, we write an integral equation which determines the area as a function of the shape of the polygon. The equations are …