Hybrid-NLIE equations, an alternative finite NLIE description for the spectral problem of the super sigma model of AdS/CFT and its gamma-deformations are derived by replacing the semi-infinite SU(2) and SU(4) parts of the AdS/CFT TBA equations by a f
ew appropriately chosen complex NLIE variables, which are coupled among themselves and to the Y-functions associated to the remaining central nodes of the TBA diagram. The integral equations are written explicitly for the ground state of the gamma-deformed system. We linearize these NLIE equations, analytically calculate the first correction to the asymptotic solution and find agreement with analogous results coming from the original TBA formalism. Our equations differ substantially from the recently published finite FiNLIE formulation of the spectral problem.
We present a method of removing all infinite sums from the various forms of the mirror TBA equations and the energy formula of the AdS/CFT spectral problem. This new formulation of the TBA system is quasi-local because Y-functions that are connected
by the TBA equations are at most next to nearest neighbors with respect to the Y-system diagram of AdS/CFT.
