On the proposed AdS dual of the critical O(N) sigma model for any dimension 2<d<4

TL;DR

This paper computes the 4-point function in the critical O(N) sigma model, supporting the AdS duality with tensor gauge fields of arbitrary even rank, and confirms the Klebanov-Polyakov hypothesis.

Contribution

It provides explicit calculations of the 4-point function at O(1/N), demonstrating the duality with tensor gauge fields in AdS for any 2<d<4.

Findings

4-point function describes exchange of tensor currents of arbitrary even rank

Supports the AdS duality with tensor gauge fields of the same rank

Derives couplings of tensor currents to auxiliary fields

Abstract

We evaluate the 4-point function of the auxiliary field in the critical O(N) sigma model at O(1/N) and show that it describes the exchange of tensor currents of arbitrary even rank l>0. These are dual to tensor gauge fields of the same rank in the AdS theory, which supports the recent hypothesis of Klebanov and Polyakov. Their couplings to two auxiliary fields are also derived.