Identification of Bulk coupling constant in Higher Spin/ABJ correspondence

TL;DR

This paper investigates the duality between higher spin theories in AdS and ABJ theory, focusing on relating bulk coupling constants to boundary parameters through stress tensor correlators computed via supersymmetric localization.

Contribution

It provides a detailed computation of the stress tensor two-point function in ABJ theory to identify the bulk coupling constant in the higher spin/ABJ duality.

Findings

Confirmed the relation between boundary parameters and bulk coupling constant.

Determined the unknown coefficient in the duality correspondence.

Supported the conjectured duality with explicit localization calculations.

Abstract

We study the conjectured duality between the $\mathcal{N}=6$ Vasiliev higher spin theory on $AdS_4$ and 3d $\mathcal{N}=6$ superconformal Chern-Simons matter theory known as the ABJ theory. We discuss how the parameters in the ABJ theory should be related to the bulk coupling constant in the Vasiliev theory. For this purpose, we compute two-point function of stress tensor in the ABJ theory by using supersymmmetry localization. Our result justifies the proposal by arXiv:1504.00365 and determine the unknown coefficient in the previous work.