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

TL;DR

This paper explores the integrable structure of certain operators in N=4 SYM and their correspondence to semi-classical string states with three angular momenta on AdS_5 x S^5, identifying a critical line and proposing duals for elliptic strings.

Contribution

It analyzes the Bethe equations for three-spin operators in N=4 SYM, identifying a critical line and proposing duals for elliptic string states with three spins.

Findings

Identification of a critical line in parameter space.

Proposal that operators above the critical line correspond to elliptic strings.

Support for the duality through perturbative calculations.

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.