The Goldstone Equivalence Theorem and AdS/CFT

TL;DR

This paper extends the Goldstone equivalence theorem within the AdS/CFT framework, relating scattering amplitudes and correlation functions for large scaling dimensions and higher spin fields.

Contribution

It generalizes the Goldstone equivalence theorem to AdS/CFT, including correlation functions, higher spin fields, and conformal blocks in various dimensions.

Findings

Correlation functions of creation and annihilation operators are related via the theorem.

Divergence of non-conserved conformal currents is approximately primary for large exchanged particle masses.

Conformal blocks satisfy an equivalence theorem when operator dimensions are large.

Abstract

The Goldstone equivalence theorem allows one to relate scattering amplitudes of massive gauge fields to those of scalar fields in the limit of large scattering energies. We generalize this theorem under the framework of the AdS/CFT correspondence. First, we obtain an expression of the equivalence theorem in terms of correlation functions of creation and annihilation operators by using an AdS wave function approach to the AdS/CFT dictionary. It is shown that the divergence of the non-conserved conformal current dual to the bulk gauge field is approximately primary when computing correlators for theories in which the masses of all the exchanged particles are sufficiently large. The results are then generalized to higher spin fields. We then go on to generalize the theorem using conformal blocks in two and four-dimensional CFTs. We show that when the scaling dimensions of the exchanged operators are large compared to both their spins and the dimension of the current, the conformal blocks satisfy an equivalence theorem.