Holographic three-point functions of semiclassical states

TL;DR

This work develops a holographic framework for three-point functions in ${\cal N}=4$ SYM when two operators are semiclassical and one is dual to a supergravity mode, and discusses the transition to a fully semiclassical regime. It relies on a hybrid first-quantized string–supergravity approach, defining a holographic OPE via the ratio $\langle \mathcal{O}_I(x)\rangle_{\mathcal{W}}$ and computing OPE coefficients through worldsheet integrals that couple to KK-reduced metric perturbations. The authors provide explicit results for chiral primaries (CPOs) and BMN operators, analyze spinning-string configurations on $S^5$, and perform a saddle-point analysis showing exponential suppression in certain regimes; they also reveal the formation of a spike on the worldsheet when vertex insertions carry $k\sim\sqrt{\lambda}$. The findings illuminate the strong-coupling structure of three-point functions in a controlled semiclassical limit, offering concrete formulas and pointing to broader directions for connecting with integrability and vertex-operator construction for non-protected states.

Abstract

We calculate the holographic three-point functions in N = 4 super-Yang-Mills theory in the case when two of the operators are semiclassical and one is dual to a supergravity mode. We further discuss the transition to the regime when all three operators are semiclassical.

Figures (3)

• Figure 1: (a) The three-point function of semiclassical operators. (b) The correlator of two semiclassical operators and a supergravity mode.
• Figure 2: The vertex operator creates an infinite spike.
• Figure 3: The string worldsheet in the vicinity of a spike.