New locally (super)conformal gauge models in Bach-flat backgrounds

Abstract

For every conformal gauge field $h_{\alpha (n)\dot{\alpha }(m)}$ in four dimensions, with $n\ge m>0$, a gauge-invariant action is known to exist in arbitrary conformally flat backgrounds. If the Weyl tensor is non-vanishing, however, gauge invariance holds for a pure conformal field in the following cases: (i) $n=m=1$ (Maxwell's field) on arbitrary gravitational backgrounds; and (ii) $n=m+1=2$ (conformal gravitino) and $n=m=2$ (conformal graviton) on Bach-flat backgrounds. It is believed that in other cases certain lower-spin fields must be introduced to ensure gauge invariance in Bach-flat backgrounds, although no closed-form model has yet been constructed (except for conformal maximal depth fields with spin $s=5/2$ and $s=3$). In this paper we derive such a gauge-invariant model describing the dynamics of a conformal gauge field $h_{\alpha (3)\dot{\alpha }}$ coupled to a self-dual two-form. Similar to other conformal higher-spin theories, it can be embedded in an off-shell superconformal gauge-invariant action. To this end, we introduce a new family of $\mathcal{N}=1$ superconformal gauge multiplets described by unconstrained prepotentials ${{\rm Y}}_{\alpha (n)}$, with $n>0$, and propose the corresponding gauge-invariant actions on conformally-flat backgrounds. We demonstrate that the $n=2$ model, which contains $h_{\alpha (3)\dot{\alpha }}$ at the component level, can be lifted to a Bach-flat background provided ${{\rm Y}}_{\alpha (2)}$ is coupled to a chiral spinor ${\Omega }_{\alpha }$. We also propose families of (super)conformal higher-derivative non-gauge actions and new superconformal operators in any curved space. Finally, through considerations based on supersymmetry, we argue that the conformal spin-3 field should always be accompanied by a conformal spin-2 field in order to ensure gauge invariance in a Bach-flat background.

arXiv comment57 pages; v3: comments, references and an appendix added, published version

References in corpus (28)

• How massless are massless fields in $Ad{S}_d$
• Conformal Higher Spin Theory
• Conformally invariant powers of the Laplacian, Q-curvature, and tractor calculus
• Effective action in a higher-spin background
• N=1 Conformal Superspace in Four Dimensions
• On limits of superstring in AdS_5 x S^5
• Bosonic conformal higher--spin fields of any symmetry
• New higher-derivative invariants in N=2 supergravity and the Gauss-Bonnet term
• On higher spin interactions with matter
• Conformal supergravity in three dimensions: New off-shell formulation
• Conformal supergravity in five dimensions: New approach and applications
• N=2 Conformal Superspace in Four Dimensions
• Invariants for minimal conformal supergravity in six dimensions
• Construction of all N=4 conformal supergravities
• Off-shell superconformal higher spin multiplets in four dimensions
• On conformal higher spin wave operators
• Component reduction in N=2 supergravity: the vector, tensor, and vector-tensor multiplets
• A dual formulation of supergravity-matter theories
• On massive tensor multiplets
• On induced action for conformal higher spins in curved background
• Conformal geometry and (super)conformal higher-spin gauge theories
• N=4 conformal supergravity: the complete actions
• Weyl Action of Two-Column Mixed-Symmetry Field and Its Factorization Around (A)dS Space
• Symmetries of supergravity backgrounds and supersymmetric field theory
• On conformal higher spins in curved background
• Comment on "The N = 3 Weyl Multiplet in Four Dimensions"
• Geometrical structure of Weyl invariants for spin three gauge field in general gravitational background in $d=4$
• Generalised conformal higher-spin fields in curved backgrounds

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• Extended superconformal higher-spin gauge theories in four dimensions
• Conformal interactions between matter and higher-spin (super)fields
• $\mathcal{N}=2$ superconformal higher-spin multiplets and their hypermultiplet couplings
• AdS superprojectors
• Conformally covariant operators of mixed-symmetry tensors and MAGs
• Generalised superconformal higher-spin multiplets
• Symmetries of $\mathcal{N}=(1,0)$ supergravity backgrounds in six dimensions
• Threshold resummation for $Z$-boson pair production at NNLO+NNLL