Correlation Functions of Sp(2n) Invariant Higher-Spin Systems

TL;DR

This paper analyzes the structure of correlation functions in Sp(2n)-invariant higher-spin systems, revealing that certain correlators are constrained to be free-theory-like due to symmetry and conservation laws.

Contribution

It demonstrates that Sp(2n) symmetry and current conservation enforce free-theory behavior in specific correlation functions of higher-spin systems across various dimensions.

Findings

3-point correlators of conserved currents and scalars are free-theory-like for n>2

Sp(2n) symmetry constrains correlation functions in higher-spin systems

The results unify understanding across different space-time dimensions

Abstract

We study the general structure of correlation functions in an Sp(2n)-invariant formulation of systems of an infinite number of higher-spin fields. For n=4,8 and 16 these systems comprise the conformal higher-spin fields in space-time dimensions D=4,6 and 10, respectively, while when n=2, one deals with conventional D=3 conformal field theories of scalars and spinors. We show that for n>2 the Sp(2n) symmetry and current conservation makes the 3-point correlators of two (rank-one or rank-two) conserved currents with a scalar operator be that of free theory.This situation is analogous to the one in conventional conformal field theories, where conservation of higher-spin currents implies that the theories are free.