This project aims to formulate the full solution to the spectral problem of the planar AdS/CFT correspondence. This will be achieved in three steps. Firstly, I will subject the recently proposed set of spectral equations (TBA equations) for the planar AdS/CFT correspondence to extensive tests and, if necessary, modify them. Secondly, I will develop new powerful tools to facilitate the computation of the energies/dimensions of the physical states from the TBA equations. This should also give a handle on the origin of the underlying integrable structures. Finally, I will attempt to motivate the spectral equations for each of the constituent theories separately. This will furnish a proof of the planar AdS/CFT correspondence as far as the spectral problem is concerned and is expected to provide a profound insight into the dynamical degrees of freedom of the gauge and string theories. The proposed research will significantly advance the state-of-the-art of the AdS/CFT correspondence and of exactly solvable quantum field theories.
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