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

TL;DR

This work constructs a coherent-state path integral for the SL(2,R) spin chain, showing that its continuum limit is a two-dimensional sigma model on the hyperboloid $SL(2,R)/U(1)$. The authors then match this spin-chain sigma model to the worldsheet dynamics of strings spinning with large angular momentum in $AdS_5\times S^5$, identifying semiclassical SL(2,R) spin-chain states with fast-spinning strings. They derive the effective action including a Wess-Zumino term, obtain classical spinning-string solutions, and recover a BMN-like spectrum in the bottom-of-hyperboloid limit. The results extend the well-known su(2) spin-chain/sigma-model correspondence to a non-compact sector and lay groundwork for higher-loop and non-planar explorations, with implications for conformal gauge theories and QCD-like regimes.

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.

Figures (1)

• Figure 1: The vector $\vec{n}_k$ moving on the hyperboloid.