What is the gravity dual of a chiral primary?

Abstract

In the AdS/CFT correspondence a chiral primary is described by a string theory solution with mass equaling angular momentum. For AdS 3× 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.