Strong coupling anomalous dimensions of = 4 super Yang-Mills

We study the strong coupling behaviour of fixed length single trace operators in the scalar SU(2) sector of = 4 SYM. We assume the recently proposed connection with a twisted half-filled Hubbard model. By explicit direct diagonalization of operators with length L = 4,6,8 we study the full perturbative multiplet of those lattice states which have a clear correspondence with gauge theory composite operators. For this multiplet, we follow the weak-strong coupling flow to free fermion states and identify in particular the precise asymptotic fermion configuration. Next, we analyze the Lieb-Wu equations of the twisted Hubbard model. For the antiferromagnetic state we derive its strong coupling expansion working at L up to 32. We also study the lightest state in the perturbative multiplet. This state is non trivial since involves complex solutions of the Lieb-Wu equations. It is particularly interesting for AdS₅ × S⁵ duality since it is dual to the folded string semiclassical solution in the thermodynamical limit. We are able to perform the full analysis and compute the next-to-next-to leading terms in the strong coupling expansion for the non trivial lengths L = 12 and L = 20. A general formula is proposed for the NLO expansion for any L = 4(2k+1), k∊.