Solving the Noether procedure for cubic interactions of higher spins in (A)dS

Light-cone gauge formulation of relativistic dynamics of a continuous-spin field propagating in the flat space is developed. Cubic interaction vertices of continuous-spin massless fields and totally symmetric arbitrary spin massive fields are studied. We consider parity invariant cubic vertices that involve one continuous-spin massless field and two arbitrary spin massive fields and parity invariant cubic vertices that involve two continuousspin massless fields and one arbitrary spin massive field. We construct the complete list of such vertices explicitly. Also we demonstrate that there are no cubic vertices describing consistent interaction of continuous-spin massless fields with arbitrary spin massless fields.

Section: Discussionmentioning

confidence: 99%

Cubic interaction vertices for continuous-spin fields and arbitrary spin massive fields

Metsaev

2017

“…One of the outstanding problems is to connect two different approaches to higher spin gravity that are presently pursued: Vasiliev's theory and the quasi-local deformed Fronsdal theory. The latter approach (see [43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58] and references therein; see also [59] for a review and more references, and [109][110][111][112][113] for more recent works on the holographic reconstruction of bulk vertices) provides a perturbatively defined deformation of the free Fronsdal action following the Noether procedure supplemented by weak locality conditions -as to ensure well-defined amplitudes built using Green's functions in anti-de Sitter spacetime with proper boundary conditions. Up to quartic order, this approach has so far been yielding holographic correlation functions corresponding to unitary free conformal field theories.…”

Section: Motivationsmentioning

confidence: 99%

4D higher spin black holes with nonlinear scalar fluctuations

Iazeolla

Sundell

2017

216

Abstract:We construct an infinite-dimensional space of solutions to Vasiliev's equations in four dimensions that are asymptotic to AdS spacetime and superpose massless scalar particle modes over static higher spin black holes. Each solution is obtained by a large gauge transformation of an all-order perturbatively defined particular solution given in a simple gauge, in which the spacetime connection vanishes, the twistor space connection is holomorphic, and all local degrees of freedom are encoded into the residual twistor space dependence of the spacetime zero-forms. The latter are expanded over two dual spaces of Fock space operators, corresponding to scalar particle and static black hole modes, equipped with positive definite sesquilinear and bilinear forms, respectively. Switching on an AdS vacuum gauge function, the twistor space connection becomes analytic at generic spacetime points, which makes it possible to reach Vasiliev's gauge, in which Fronsdal fields arise asymptotically, by another large transformation given here at first order. The particle and black hole modes are related by a twistor space Fourier transform, resulting in a black hole backreaction already at the second order of classical perturbation theory. We speculate on the existence of a fine-tuned branch of moduli space that is free from black hole modes and directly related to the quasi-local deformed Fronsdal theory. Finally, we comment on a possible interpretation of the higher spin black hole solutions as black-hole microstates.

“…Finding HS interactions in (A)dS has been the aim of our previous investigations [34][35][36][37], where, making use of the ambient-space formalism [38,39], we provided the transverse and traceless (TT) parts of all possible cubic interactions involving massive and massless totally-symmetric HS fields. The key point of our construction was to recast the consistency conditions for the cubic vertices into a system of linear partial differential equations (PDEs), 3 whose solutions are in one-to-one correspondence to the consistent couplings.…”

Section: Introductionmentioning

confidence: 99%

Generating functions of (partially-)massless higher-spin cubic interactions

Joung

López

Taronna

2013

Self Cite

Generating functions encoding cubic interactions of (partially-)massless higherspin fields are provided within the ambient-space formalism. They satisfy a system of higher-order partial differential equations that can be explicitly solved due to their factorized form. We find that the number of consistent couplings increases whenever the squares of the field masses take some integer values (in units of the cosmological constant) and satisfy certain conditions. Moreover, it is shown that only the supplemental solutions can give rise to non-Abelian deformations of the gauge symmetries. The presence of these conditions on the masses is a distinctive feature of (A)dS interactions that has in general no direct counterpart in flat space.