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What is the gravity dual of a chiral primary?

Oleg Lunin, Samir D. Mathur, Ashish Saxena

TL;DR

The authors determine the gravity duals of chiral primaries in the D1-D5 system by exploiting the FP (F1-P) description and its spectral flow to D1-D5, yielding a general class of chiral primary metrics that include and unify previously studied cases. They show conical defect geometries correspond to states built from identical twist operators, while Aichelburg-Sexl type solutions arise from highly dispersed twist orders; giant gravitons correspond to disassociated D1-D5 configurations rather than true chiral primaries. Their analysis reveals that the large-distance behavior of the supergravity fields is directly linked to the dispersion in the orders and spins of the twist operators creating the dual CFT state. This work provides a concrete bridge between bulk asymptotics and boundary operator content, highlighting how geometric data encodes the detailed structure of the CFT state in AdS/CFT for $AdS_3\times S^3$.

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.

What is the gravity dual of a chiral primary?

TL;DR

The authors determine the gravity duals of chiral primaries in the D1-D5 system by exploiting the FP (F1-P) description and its spectral flow to D1-D5, yielding a general class of chiral primary metrics that include and unify previously studied cases. They show conical defect geometries correspond to states built from identical twist operators, while Aichelburg-Sexl type solutions arise from highly dispersed twist orders; giant gravitons correspond to disassociated D1-D5 configurations rather than true chiral primaries. Their analysis reveals that the large-distance behavior of the supergravity fields is directly linked to the dispersion in the orders and spins of the twist operators creating the dual CFT state. This work provides a concrete bridge between bulk asymptotics and boundary operator content, highlighting how geometric data encodes the detailed structure of the CFT state in AdS/CFT for .

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.

Paper Structure

This paper contains 26 sections, 108 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The issue
  3. Results
  4. The metrics for general chiral primaries
  5. The D1-D5 and FP systems
  6. Spectral flow
  7. The detailed FP $\rightarrow$ D1-D5 map
  8. Metrics for special cases of interest
  9. Case I: $AdS_3\times S^3$
  10. Case II: The conical defect metrics
  11. Case III - the Aichelburg-Sexl metric
  12. Giant gravitons
  13. The FP representation of a giant graviton
  14. Geometry produced by a giant graviton.
  15. Asymptotic behavior of the supergravity solution and its relation to dispersions in the CFT dual
  16. ...and 11 more sections

Figures (3)

  • Figure 1: (a) The F string opened up to its full length, rotating in a helix with a single turn; this gives $AdS_3\times S^3$. (b) The F string executing a helix in the second harmonic; this gives a conical defect metric.
  • Figure 2: (a) The F string executes one turn of a helix and then stays at a constant location. (b) The constant part of the string is broken into several segments which are interspersed with the curved part; this gives the Aichelburg-Sexl solution.
  • Figure 3: (a) In all bound states the F string closes after $n_5$ turns around the $y$ direction. (b) One turn of the F string is broken off; this gives a giant graviton.