Circular and Folded Multi-Spin Strings in Spin Chain Sigma Models

TL;DR

This paper derives classical string solutions with multiple spins from spin chain sigma models, connecting integrable spin chains to string theory in AdS_5 x S^5 and demonstrating energy correspondences.

Contribution

It explicitly constructs multi-spin string solutions within spin chain sigma models at one- and two-loop orders, extending the understanding of the AdS/CFT correspondence.

Findings

Recovered classical circular string solutions with two spins from spin chain models.

Constructed folded string solutions with one AdS_5 spin and one S^5 spin.

Demonstrated energy matching for three-spin circular string solutions.

Abstract

From the SU(2) spin chain sigma model at the one-loop and two-loop orders we recover the classical circular string solution with two S^5 spins (J_1, J_2) in the AdS_5 x S^5 string theory. In the SL(2) sector of the one-loop spin chain sigma model we explicitly construct a solution which corresponds to the folded string solution with one AdS_5 spin S and one S^5 spin J. In the one-loop general sigma model we demonstrate that there exists a solution which reproduces the energy of the circular constant-radii string solution with three spins (S_1, S_2, J).