D-branes and orbit average

Peihe Yang,Jun-Bao Wu,Shota Komatsu,Yunfeng Jiang

doi:10.21468/scipostphys.12.2.055

Abstract

We study correlation functions of D-branes and a supergravity mode in AdS, which are dual to structure constants of two sub-determinant operators with large charge and a BPS single-trace operator. Our approach is inspired by the large charge expansion of CFT and resolves puzzles and confusions in the literature on the holographic computation of correlation functions of heavy operators. In particular, we point out two important effects which are often missed in the literature; the first one is an average over classical configurations of the heavy state, which physically amounts to projecting the state to an eigenstate of quantum numbers. The second one is the contribution from wave functions of the heavy state. To demonstrate the power of the method, we first analyze the three-point functions in N=4 super Yang-Mills and reproduce the results in field theory from holography, including the cases for which the previous holographic computation gives incorrect answers. We then apply it to ABJM theory and make solid predictions at strong coupling. Finally we comment on possible applications to states dual to black holes and fuzzballs.

Highlights

In particular in [4], they analyzed the extremal three-point functions and found that the results in the gauge theory and the holography look similar but do not quite match. This was rather puzzling since the structure constants of 1/2 BPS operators are known to be protected [9,10] and one would naively expect the two results to match perfectly. They speculated that the mismatch is due to the inability of sub-determinant operators to interpolate between a point-like graviton and a giant graviton
No definite conclusion was made since the three-point functions of BPS operators in ABJM theory are not protected and one cannot directly compare the results in the gauge theory and in the holography
We feel that comparing the extremal three-point functions between the gauge theory and the supergravity is an ill-posed question

Summary

Introduction

In particular in [4], they analyzed the extremal three-point functions and found that the results in the gauge theory and the holography look similar but do not quite match This was rather puzzling since the structure constants of 1/2 BPS operators are known to be protected [9,10] and one would naively expect the two results to match perfectly. It was realized in [6, 8] that the holographic computation for the extremal threepoint functions involves a (zero prefactor) × (divergent integral) structure If one regularizes this quantity and takes a careful limit, it produces a finite correction which makes the final result match with the gauge theory answer. The “resolution" proposed in the literature is not satisfactory for several reasons:

Results

Discussion

Conclusion