Slow-string limit and "antiferromagnetic" state in AdS/CFT

TL;DR

This paper explores a slow-string limit in AdS/CFT, connecting a specific string solution to the antiferromagnetic state in the dual gauge theory, and derives an effective sine-Gordon model relevant to the gauge/string correspondence.

Contribution

It introduces a slow-moving string limit that approximates the antiferromagnetic state in the dual gauge theory and derives an effective sine-Gordon model from string and Hubbard model analyses.

Findings

String solution with winding number approximates the antiferromagnetic state.

Effective sine-Gordon model describes the near-solution dynamics.

Connections established between string theory and Hubbard model continuum limit.

Abstract

We discuss a slow-moving limit of a rigid circular equal-spin solution on R x S^3. We suggest that the solution with the winding number equal to the total spin approximates the quantum string state dual to the maximal-dimension ``antiferromagnetic'' state of the SU(2) spin chain on the gauge theory side. An expansion of the string action near this solution leads to a weakly coupled system of a sine-Gordon model and a free field. We show that a similar effective Hamiltonian appears in a certain continuum limit from the half-filled Hubbard model that was recently suggested to describe the all-order dilatation operator of the dual gauge theory in the SU(2) sector. We also discuss some other slow-string solutions with one spin component in AdS_5 and one in S^5.