SL(2) spin chain and spinning strings on AdS_5xS^5

TL;DR

This paper establishes a connection between SL(2,R) spin chains and spinning strings in AdS_5xS^5 by deriving a sigma model from the spin chain and identifying it with semiclassical string states.

Contribution

It introduces a coherent state representation for the SL(2,R) spin chain and links it to spinning string solutions in AdS_5xS^5, bridging integrable spin chains and string theory.

Findings

Derived the SL(2,R) spin chain sigma model.

Connected the sigma model to spinning string solutions.

Identified semiclassical coherent states with string states.

Abstract

We derive the coherent state representation of the integrable spin chain Hamiltonian with symmetry group SL(2,R). By passing to the continuum limit, we find a spin chain sigma model describing a string moving on the hyperboloid SL(2,R)/U(1). The same sigma model is found by considering strings rotating with large angular momentum in AdS_5xS^5. The spinning strings are identified with semiclassical coherent states built out of SL(2,R) spin chain states.