Three-spin Strings on AdS_5 x S^5 from N=4 SYM

TL;DR

The paper investigates one-loop anomalous dimensions of holomorphic three-spin operators in N=4 SYM using the integrable SO(6) spin chain, mapping to semi-classical three-spin strings on AdS5×S5. By analyzing Bethe-root distributions in the thermodynamic limit, it reveals a line of critical points that separates distinct string-dual regimes, with the high-β side corresponding to circular elliptic three-spin strings, corroborated by perturbative matching to string energies. The work connects four-cut integral equations to elliptic (and potentially hyper-elliptic) structures and explains how the dual string interpretation changes across the line. It also outlines avenues for exact solutions, higher conserved charges, and deeper links to the string sigma-model.

Abstract

Using the integrable spin chain picture we study the one-loop anomalous dimension of certain single trace scalar operators of N=4 SYM expected to correspond to semi-classical string states on AdS_5 x S^5 with three large angular momenta (J_1,J_2,J_3) on S^5. In particular, we investigate the analyticity structure encoded in the Bethe equations for various distributions of Bethe roots. In a certain region of the parameter space our operators reduce to the gauge theory duals of the folded string with two large angular momenta and in another region to the duals of the circular string with angular momentum assignment (J,J',J'), J>J'. In between we locate a critical line. We propose that the operators above the critical line are the gauge theory duals of the circular elliptic string with three different spins and support this by a perturbative calculation.