Sergio Hörtner

Higher spin conformal geometry in three dimensions and prepotentials for higher spin gauge fields

A bstractWe study systematically the conformal geometry of higher spin bosonic gauge fields in three spacetime dimensions. We recall the definition of the Cotton tensor for higher spins and establish a number of its properties that turn out to be key in solving in terms of prepotentials the constraint equations of the Hamiltonian (3 + 1) formulation of four-dimensional higher spin gauge fields. The prepotentials are shown to exhibit higher spin conformal symmetry. Just as for spins 1 and 2, they provide a remarkably simple, manifestly duality invariant formulation of the theory. While the higher spin conformal geometry is developed for arbitrary bosonic spin, we explicitly perform the Hamiltonian analysis and derive the solution of the constraints only in the illustrative case of spin 3. In a separate publication, the Hamiltonian analysis in terms of prepotentials is extended to all bosonic higher spins using the conformal tools of this paper, and the same emergence of higher spin conformal symmetry is confirmed.

Gravitational Electric-Magnetic Duality, Gauge Invariance and Twisted Self-Duality

The concept of electric–magnetic duality can be extended to linearized gravity. It has indeed been established that in four dimensions, the Pauli–Fierz action (quadratic part of the Einstein–Hilbert action) can be cast in a form that is manifestly invariant under duality rotations in the internal 2-plane of the spacetime curvature and its dual. In order to achieve this manifestly duality-invariant form, it is necessary to introduce two ‘prepotentials’, which form a duality multiplet. These prepotentials enjoy interesting gauge invariance symmetries, which are, for each, linearized diffeomorphisms and linearized Weyl rescalings. The purpose of this note is twofold: (i) to rewrite the manifestly-duality invariant action obtained in previous work in a way that makes its gauge invariances also manifest, (ii) to explicitly show that the equations of motion derived from that action can be interpreted as twisted self-duality conditions on the curvature tensors of the two metrics obtained from the two prepotentials.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Higher spin theories and holography’.

Higher-spin charges in Hamiltonian form. I. Bose fields

A bstractWe study asymptotic charges for symmetric massless higher-spin fields on Anti de Sitter backgrounds of arbitrary dimension within the canonical formalism. We first analyse in detail the spin-3 example: we cast Fronsdal’s action in Hamiltonian form, we derive the charges and we propose boundary conditions on the canonical variables that secure their finiteness. We then extend the computation of charges and the characterisation of boundary conditions to arbitrary spin.

Higher-spin charges in Hamiltonian form. II. Fermi fields

A bstractWe build the asymptotic higher-spin charges associated with “improper” gauge transformations for fermionic higher-spin gauge fields on Anti de Sitter backgrounds of arbitrary dimension. This is achieved within the canonical formalism. We consider massless fields of spin s+1/2, described by a symmetric spinor-tensor of rank s in the Fang-Fronsdal approach. We begin from a detailed analysis of the spin 5/2 example, for which we cast the Fang-Fronsdal action in Hamiltonian form, we derive the charges and we propose boundary conditions on the canonical variables that secure their finiteness. We then extend the computation of charges and the characterisation of boundary conditions to arbitrary half-integer spin. Our construction generalises to higher-spin fermionic gauge fields the known Hamiltonian derivation of supercharges in AdS supergravity.

A deformation of the Curtright action

We present a deformation of the action principle for a free tensor field of mixed symmetry (2,1) –the Curtright action, a dual formulation of five-dimensional linearized gravity. It is constructed as the dual theory of the Einstein-Hilbert action linearized around a de Sitter background, and its derivation relies on the use of the two-potential formalism as an intermediate step. The resulting action principle is spatially non-local and space-time covariance is not manifest, thus overcoming previous no-go results.We present a deformation of the action principle for a free tensor field of mixed symmetry (2,1) --the Curtright action, a dual formulation of five-dimensional linearized gravity. It is constructed as the dual theory of the Einstein-Hilbert action linearized around a de Sitter background, and its derivation relies on the use of the two-potential formalism as an intermediate step. The resulting action principle is spatially non-local and space-time covariance is not manifest, thus overcoming previous no-go results.