Circular strings, magnons, plane waves and local quenches in BTZ

TL;DR

This paper demonstrates that string states like circular strings, magnons, and plane waves in $AdS_3 \times S^3 \times M$ have counterparts in BTZ geometry, which correspond to local quenches in the dual thermal CFT, revealing a deep connection between string excitations and CFT dynamics.

Contribution

The authors establish a map connecting classical string solutions in $AdS_3$ to states in BTZ geometry, and interpret these as local quenches in the dual CFT, providing new insights into holographic correspondence.

Findings

String states in $AdS_3$ have BTZ counterparts with related charges.

BTZ states correspond to local quenches in the dual CFT.

The map relates $SL(2,R)$ charges via a boost, linking string solutions to CFT excitations.

Abstract

We show that string theory on the geometry $BTZ\times S^3\times M$ supported with either Neveu-Schwarz flux or Ramond flux admits states which obey identical dispersion relations to those of classical solutions like circular strings, giant magnons, or plane wave excitations in the geometry $ AdS_3 \times S^3 \times M$. Here, $M$ can be $T^4$, $K3$, or $S^3\times S^1$. This is made possible by the map, which takes the particle at the origin of $AdS_3$ with angular momentum along one of the angles of $S_3$ to a particle falling into the BTZ horizon. We use this map to construct circular strings, magnons, as well as plane waves in the BTZ geometry. We show that the $SL(2, R)$ charges of these states on $AdS_3$ and that of the corresponding states in the BTZ geometry are related by a boost. The dual description of these states in the BTZ geometry are local quenches in the thermal CFT. These quenches carry energy density, $R$-charges, non-trivial expectation value of the marginal operator dual to the dilaton and move on the light cone in CFT. In general, the left and the right moving quenches are not symmetric.