${\cal N}=2$ Higher Spins by Harmonic Superspace Methods

TL;DR

This work surveys the use of harmonic ${ m N}=2$ superspace to formulate off-shell higher-spin multiplets in four dimensions, deriving analytic gauge potentials for spins including ${f s}=2$ and ${f s}=3$ and constructing manifestly ${ m N}=2$ supersymmetric couplings to hypermultiplets. It develops both conformal and non-conformal higher-spin interactions within the harmonic superspace framework, culminating in an invariant action for an infinite tower of higher spins in a conformal ${ m N}=2$ supergravity background. The paper also addresses superconformal extensions, the structure of cubic vertices, and the pathway toward AdS$_4$ backgrounds, outlining key challenges for nonlinear completion, half-integer spins, and fully gauged ${ m N}=2$ higher-spin theories. Together, these results establish a systematic, off-shell, ${ m N}=2$ approach to higher-spin dynamics with potential links to AdS/CFT and quantum consistency checks.

Abstract

Harmonic ${\cal N}=2$ superspace was discovered in 1984 as the powerful tool of the geometric superfield off-shell description of ${\cal N}=2, 4D$ supersymmetric field theories with the maximal spins 1, 2, and 1/2 (${\cal N}=2$ Yang-Mills theories, supergravity and matter hypermultiplets). My talk is a brief account of the basic achievements of the harmonic methods, including the newest applications in ${\cal N}=2$ theories of higher spins.