Gravitating spinning strings in AdS$_3$

TL;DR

This paper studies classical spinning strings in AdS$_3$ within the AdS/CFT framework, revealing their gravitational back-reaction at high spin and connecting their spectrum to extremal BTZ black holes.

Contribution

It constructs coupled solutions of spinning strings and gravity in AdS$_3$, showing their maximal spin limit and relation to BTZ black holes, advancing understanding of string-gravity interactions.

Findings

Strings exhibit significant back-reaction at high spin.

Solutions exist only below a maximum spin J_max.

Approaching J_max, solutions resemble extremal BTZ black holes.

Abstract

In the AdS/CFT correspondence, single trace operators of large-$N$ gauge theories at large spin $J$ can be described by classical spinning strings, giving a geometric and classical description of their spectrum at strong coupling. We observe that in AdS$_3$ these strings have significant gravitational back-reaction at sufficiently large spin, since the gravitational force does not decay at long distances. We construct solutions for folded spinning strings coupled to gravity in AdS$_3$ and compute their spectrum, corresponding to the leading Regge trajectory of Virasroro primary operators. These solutions exist only below a maximal spin $J<J_\mathrm{max}$, and as $J\to J_\mathrm{max}$ the solution approaches an extremal rotating BTZ black hole.