Strong coupling from the Hubbard model

Abstract

It was recently observed that the one dimensional half-filled Hubbard model reproduces the known part of the perturbative spectrum of planar N=4 super Yang-Mills in the SU(2) sector. Assuming that this identification is valid beyond perturbation theory, we investigate the behavior of this spectrum as the 't Hooft parameter λbecomes large. We show that the full dimension Δof the Konishi superpartner is the solution of a sixth order polynomial while Δfor a bare dimension 5 operator is the solution of a cubic. In both cases the equations can be solved easily as a series expansion for both small and large λand the equations can be inverted to express λas an explicit function of Δ. We then consider more general operators and show how Δdepends on λin the strong coupling limit. We are also able to distinguish those states in the Hubbard model which correspond to the gauge invariant operators for all values of λ. Finally, we compare our results with known results for strings on AdS_5\times S^5, where we find agreement for a range of R-charges.