From Higher Spins to Strings: A Primer

TL;DR

This paper provides a comprehensive pedagogical overview of higher-spin fields, their mathematical formulations, interactions, and connections with string theory, highlighting recent advances and unresolved issues in the field.

Contribution

It offers a detailed review of higher-spin theory, including covariant equations, interaction constraints, unfolded formalism, and implications for string dualities, serving as an introductory resource.

Findings

Review of higher-spin field equations and representations

Analysis of no-go and yes-go interaction results

Derivation of boundary-to-bulk propagator in AdS_4

Abstract

A contribution to the collection of reviews "Introduction to Higher Spin Theory" edited by S. Fredenhagen, this introductory article is a pedagogical account of higher-spin fields and their connections with String Theory. We start with the motivations for and a brief historical overview of the subject. We discuss the Wigner classifications of unitary irreducible Poincar\'e-modules, write down covariant field equations for totally symmetric massive and massless representations in flat space, and consider their Lagrangian formulation. After an elementary exposition of the AdS unitary representations, we review the key no-go and yes-go results concerning higher-spin interactions, e.g., the Velo-Zwanziger acausality and its string-theoretic resolution among others. The unfolded formalism, which underlies Vasiliev's equations, is then introduced to reformulate the flat-space Bargmann-Wigner equations and the AdS massive-scalar Klein-Gordon equation, and to state the "central on-mass-shell theorem". These techniques are used for deriving the unfolded form of the boundary-to-bulk propagator in $AdS_4$, which in turn discloses the asymptotic symmetries of (supersymmetric) higher-spin theories. The implications for string-higher-spin dualities revealed by this analysis are then elaborated.