On (spinor)-helicity and bosonization in $AdS_4/CFT_3$

TL;DR

This paper develops a comprehensive AdS4/CFT3 dictionary for spinning fields using spinor-helicity variables, linking correlation functions, higher spin theories, and bosonization dualities through a unified framework.

Contribution

It introduces a complete AdS4/CFT3 dictionary for spinning fields in the spinor-helicity basis, enabling scalarization of contact vertices and elucidating the relation to bosonization duality.

Findings

Unified framework for AdS4/CFT3 spinning fields

Explicit dictionary for higher spin and gauge theories

Connection between bosonization and EM-duality transformations

Abstract

Helicity is a useful concept both for AdS${}_4$ and CFT${}_3$ studies. We work out the complete AdS${}_4$/CFT${}_3$ dictionary for spinning fields/operators in the spinor-helicity base that allows one to scalarize any $n$-point contact vertex. AdS${}_4$-vertices encode correlation functions of conserved currents, stress-tensor and, more generally, higher spin currents in a simple way. We work out the dictionary for Yang-Mills- and gravity-type theories with higher derivative corrections as well as some higher spin examples and exemplify the relation to the three-dimensional bosonization duality. The bosonization can be understood as a simple surgery: vertices/correlators are built via an EM-duality transformation by sewing together (anti)-Chiral higher spin gravities, to whose existence the three-dimensional bosonization duality can be attributed (up to the proof of uniqueness).