Duality-invariant (super)conformal higher-spin models

Abstract

We develop a general formalism of duality rotations for bosonic conformal spin-$s$ gauge fields, with $s\ge 2$, in a conformally flat four-dimensional spacetime. In the $s=1$ case this formalism is equivalent to the theory of $\mathsf{U}(1)$ duality-invariant nonlinear electrodynamics developed by Gaillard and Zumino, Gibbons and Rasheed, and generalised by Ivanov and Zupnik. For each integer spin $s\ge 2$ we demonstrate the existence of families of conformal $\mathsf{U}(1)$ duality-invariant models, including a generalisation of the so called ModMax Electrodynamics ($s=1$). Our bosonic results are then extended to the $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetric cases. We also sketch a formalism of duality rotations for conformal gauge fields of Lorentz type $(m/2,n/2)$, for positive integers $m$ and $n$.

42 pages; v5: typos in eqs. (2.15) and (2.16) corrected

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Cited by in corpus (6)

• Introductory Notes on Non-linear Electrodynamics and its Applications
• Root-$T\overline{T}$ Deformations in Two-Dimensional Quantum Field Theories
• Accelerated Black Holes beyond Maxwell's Electrodynamics
• Stress Tensor Flows, Birefringence in Non-Linear Electrodynamics, and Supersymmetry
• Extended superconformal higher-spin gauge theories in four dimensions
• On Current-Squared Flows and ModMax Theories