What is the gravity dual of a chiral primary?

TL;DR

This paper explores the supergravity solutions corresponding to chiral primaries in AdS_3 x S^3, identifying special metric families and their CFT duals, revealing how different geometries relate to twist operator configurations.

Contribution

It classifies supergravity solutions for chiral primaries, linking geometric limits to specific CFT twist operator states and showing how giant gravitons differ from other configurations.

Findings

Conical defect metrics correspond to identical twist operators in the CFT.

Aichelburg-Sexl metrics relate to a wide dispersion of twist operators.

Giant graviton solutions fragment the D1-D5 system, differing from other solutions.

Abstract

In the AdS/CFT correspondence a chiral primary is described by a supergravity solution with mass equaling angular momentum. For AdS_3 X S^3 we are led to consider three special families of metrics with this property: metrics with conical defects, Aichelburg-Sexl type metrics generated by rotating particles, and metrics generated by giant gravitons. We find that the first two of these are special cases of the complete family of chiral primary metrics which can be written down using the general solution in hep-th/0109154, but they correspond to two extreme limits - the conical defect metrics map to CFT states generated by twist operators that are all identical, while the Aichelburg-Sexl metrics yield a wide dispersion in the orders of these twists. The giant graviton solutions in contrast do not represent configurations of the D1-D5 bound state; they correspond to fragmenting this system into two or more pieces. We look at the large distance behavior of the supergravity fields and observe that the excitation of these fields is linked to the existence of dispersion in the orders and spins of the twist operators creating the chiral primary in the CFT.