Arbitrary spin conformal fields in (A)dS

2014/04/30 by R.R. Metsaev, R. R. Metsaev
Mathematics · Physics and Astronomy · #BRST quantization #Black Holes and Theoretical Physics #Boundary conformal field theory #Boundary value problem #Conformal anomaly #Conformal gravity #Conformal map #Conformal symmetry #Cosmology and Gravitation Theories #Gauge symmetry #Gauge theory #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Neumann boundary condition #Noncommutative and Quantum Gravity Theories #Physics #Primary field #Quantum mechanics #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2014.06.013

published as Nucl. Phys. B885 (2014) 734-771 · 38 pages, LaTeX-2e. v2: In sections 5-8, discussion of various technical details added. Typos corrected. References added

openalex publication_date 2014/06/18 · arxiv created 2014/07/02 · arxiv updated 2014/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Totally symmetric arbitrary spin conformal fields in (A)dS space of even dimension greater than or equal to four are studied. Ordinary-derivative and gauge invariant Lagrangian formulation for such fields is obtained. Gauge symmetries are realized by using auxiliary fields and Stueckelberg fields. We demonstrate that Lagrangian of conformal field is decomposed into a sum of gauge invariant Lagrangians for massless, partial-massless, and massive fields. We obtain a mass spectrum of the partial-massless and massive fields and confirm the conjecture about the mass spectrum made in the earlier literature. In contrast to conformal fields in flat space, the kinetic terms of conformal fields in (A)dS space turn out to be diagonal with respect to fields entering the Lagrangian. Explicit form of conformal transformation which maps conformal field in flat space to conformal field in (A)dS space is obtained. Covariant Lorentz-like and de-Donder like gauge conditions leading to simple gauge-fixed Lagrangian of conformal fields are proposed. Using such gauge-fixed Lagrangian, which is invariant under global BRST transformations, we explain how the partition function of conformal field is obtained in the framework of our approach.

Citations

• On Massive High Spin Particles in (A)dS
• Ultraviolet behaviour of higher spin gauge field propagators and one loop mass renormalization
• Mixed-symmetry tensor conserved currents and AdS/CFT correspondence
• On gravitational interactions for massive higher spins in AdS3
• Black holes in six-dimensional conformal gravity
• Geometric formulation for partially massless fields
• CFT adapted gauge invariant formulation of massive arbitrary spin fields in AdS
• Lagrangian formulation for free mixed-symmetry bosonic gauge fields in (A)dSd
• Bosonic conformal higher-spin fields of any symmetry
• A Quartic Conformally Covariant Differential Operator for Arbitrary Pseudo-Riemannian Manifolds (Summary)
• On massive spin 2 electromagnetic interactions
• Gauge fields in (A)dS d within the unfolded approach: algebraic aspects
• On electromagnetic interactions for massive mixed symmetry field
• A classification of local Weyl invariants in D = 8
• Ordinary-derivative formulation of conformal low-spin fields
• Tensor Gauge Fields in Arbitrary Representations of GL(D, ℝ) : II. Quadratic Actions
• Elements of Vasiliev theory