Tailoring Three-Point Functions and Integrability III. Classical Tunneling

TL;DR

This paper calculates three-point functions involving classical and BPS operators in N=4 SYM, revealing a tunneling interpretation and connecting integrability with a long-range Ising model solution.

Contribution

It introduces a classical tunneling framework for three-point functions and simplifies Bethe state inner products in a classical limit, also solving a new long-range Ising model.

Findings

Three-point functions exponentiate as classical tunneling processes.

Simplified inner products of Bethe states in the classical limit.

Solved a long-range Ising model in the thermodynamic limit.

Abstract

We compute three-point functions between one large classical operator and two large BPS operators at weak coupling. We consider operators made out of the scalars of N=4 SYM, dual to strings moving in the sphere. The three-point function exponentiates and can be thought of as a classical tunneling process in which the classical string-like operator decays into two classical BPS states. From an Integrability/Condensed Matter point of view, we simplified inner products of spin chain Bethe states in a classical limit corresponding to long wavelength excitations above the ferromagnetic vacuum. As a by-product we solved a new long-range Ising model in the thermodynamic limit.