D-branes and Orbit Average

TL;DR

This paper introduces a novel holographic method for computing correlation functions involving heavy operators by averaging over classical configurations and including wave function contributions, resolving previous discrepancies.

Contribution

It develops a new approach inspired by large charge expansion, accurately computing correlators of heavy states in AdS/CFT, and applies it to both $ ext{N}=4$ SYM and ABJM theories.

Findings

Reproduces known field theory results for three-point functions in $ ext{N}=4$ SYM

Provides new predictions for ABJM theory at strong coupling

Addresses and corrects previous holographic computation issues

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 $\mathcal{N}=4$ 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.