Higher-spin Cotton tensors and massive gauge-invariant actions in AdS${}_3$

Abstract

In a conformally flat three-dimensional spacetime, the linearised higher-spin Cotton tensor ${\mathfrak{C}}_{\alpha (n)}(h)$ is the unique conserved conformal current which is a gauge-invariant descendant of the conformal gauge prepotential $h_{\alpha (n)}$. The explicit form of ${\mathfrak{C}}_{\alpha (n)}(h)$ is well known in Minkowski space. Here we solve the problem of extending the Minkowskian result to the case of anti-de Sitter (AdS) space and derive a closed-form expression for ${\mathfrak{C}}_{\alpha (n)}(h)$ in terms of the AdS Lorentz covariant derivatives. It is shown that every conformal higher-spin action $S_{\text{CS}}^{(n)}[h]\propto \int {\text{d}}^{3}xe{h}^{\alpha (n)}{\mathfrak{C}}_{\alpha (n)}(h)$ factorises into a product of $(n-1)$ first-order operators that are associated with the spin-$n/2$ partially massless AdS values. Our findings greatly facilitate the on-shell analysis of massive higher-spin gauge-invariant actions in AdS${}_3$. The main results are extended to the case of $\mathcal{N}=1$ AdS supersymmetry. In particular, we derive simple expressions for the higher-spin super-Cotton tensors in AdS${}_3$.

arXiv comment44 pages; V2: comments added and typos corrected; V3: published version

References in corpus (66)

• Partial Masslessness of Higher Spins in (A)dS
• Gauge Invariances and Phases of Massive Higher Spins in (A)dS
• Null Propagation of Partially Massless Higher Spins in (A)dS and Cosmological Constant Speculations
• How massless are massless fields in $Ad{S}_d$
• Conformal Higher Spin Theory
• Spectrum of D=6, N=4b Supergravity on AdS_3 x S^3
• Effective action in a higher-spin background
• Geometric Formulation for Partially Massless Fields
• Massive 3D Supergravity
• New supergravities with central charges and Killing spinors in 2+1 dimensions
• Higher order singletons, partially massless fields and their boundary values in the ambient approach
• On partition function and Weyl anomaly of conformal higher spin fields
• N=1 Conformal Superspace in Four Dimensions
• Gauge invariant formulation of massive totally symmetric fermionic fields in (A)dS space
• On limits of superstring in AdS_5 x S^5
• Frame-like gauge invariant formulation for massive high spin particles
• Off-shell supergravity-matter couplings in three dimensions
• Arbitrary Spin Representations in de Sitter from dS/CFT with Applications to dS Supergravity
• Bosonic conformal higher--spin fields of any symmetry
• On Higher Derivatives in 3D Gravity and Higher Spin Gauge Theories
• The General Supersymmetric Solution of Topologically Massive Supergravity
• Partition function of free conformal higher spin theory
• Conformal supergravity in three dimensions: New off-shell formulation
• Conformal supergravity in three dimensions: Off-shell actions
• Conformal Operators for Partially Massless States
• On matter-free Higher Spin Gravities in 3d: (partially)-massless fields and general structure
• Invariants for minimal conformal supergravity in six dimensions
• Gauge invariant two-point vertices of shadow fields, AdS/CFT, and conformal fields
• Off-shell massive N=1 supermultiplets in three dimensions
• Three-dimensional (p,q) AdS superspaces and matter couplings
• N=6 superconformal gravity in three dimensions from superspace
• On triviality of S-matrix in conformal higher spin theory
• New Conformal Higher Spin Gravities in $3d$
• Off-shell superconformal higher spin multiplets in four dimensions
• On conformal higher spin wave operators
• Arbitrary spin conformal fields in (A)dS
• A note on higher-derivative actions for free higher-spin fields
• Gauge invariant Lagrangian formulation of massive higher spin fields in (A)dS_3 space
• Higher Spin Conformal Geometry in Three Dimensions and Prepotentials for Higher Spin Gauge Fields
• N=6 conformal supergravity in three dimensions
• Higher derivative couplings and massive supergravity in three dimensions
• Higher spin super-Cotton tensors and generalisations of the linear-chiral duality in three dimensions
• Conformal supergravities as Chern-Simons theories revisited
• New Unfolded Higher Spin Systems in $Ad{S}_3$
• A spin-4 analog of 3D massive gravity
• On induced action for conformal higher spins in curved background
• Frame-like gauge invariant Lagrangian formulation of massive fermionic higher spin fields in AdS_3 space
• Conformal geometry and (super)conformal higher-spin gauge theories
• Off-shell higher spin N=2 supermultiplets in three dimensions
• On the Minimal Model of Anyons
• Lagrangian description of massive higher spin supermultiplets in AdS_3 space
• Topologically massive higher spin gauge theories
• Weyl Action of Two-Column Mixed-Symmetry Field and Its Factorization Around (A)dS Space
• On Critical Massive (Super)Gravity in adS3
• Prepotentials for N=2 conformal supergravity in three dimensions
• On conformal higher spins in curved background
• The non-linear coupled spin 2 - spin 3 Cotton equation in three dimensions
• The Schouten tensor as a connection in the unfolding of 3D conformal higher-spin fields
• Spin projection operators and higher-spin Cotton tensors in three dimensions
• Scattering of conformal higher spin fields
• On the conformal higher spin unfolded equation for a three-dimensional self-interacting scalar field
• On the structure of the conformal higher-spin wave operators
• Spin projection operators in (A)dS and partial masslessness
• AdS superprojectors
• Geometrical structure of Weyl invariants for spin three gauge field in general gravitational background in $d=4$
• Three-dimensional conformal geometry and prepotentials for four-dimensional fermionic higher-spin fields

Cited by in corpus (4)

• On higher spin analogues of linearized Topologically Massive Gravity and linearized "New Massive Gravity"
• Superfield approach to interacting N=2 massive and massless supermultiplets in 3d flat space
• On equivalence of gauge-invariant models for massive integer-spin fields
• AdS (super)projectors in three dimensions and partial masslessness