Lagrangian formulation of higher spin theories on AdS space

Cubic couplings between a complex scalar field and a tower of symmetric tensor gauge fields of all ranks are investigated on any constant curvature spacetime of dimension d 3. Following Noether's method, the gauge fields interact with the scalar field via minimal coupling to the conserved currents. A symmetric conserved current, bilinear in the scalar field and containing up to r derivatives, is obtained for any rank r 1 from its flat spacetime counterpart in dimension d + 1, via a radial dimensional reduction valid precisely for the mass-square domain of unitarity in (anti) de Sitter spacetime of dimension d. The infinite collection of conserved currents and cubic vertices are summarized in a compact form by making use of generating functions and of the Weyl/Wigner quantization on constant curvature spaces.

Section: Jhep11(2010)116mentioning

confidence: 89%

“…In the late seventies, the ambient formulation had already been used by Fronsdal [14] in the context of higher-spin gauge theories and, by now, this technique has become standard and has found a large number of applications in this area (see e.g. [15][16][17][18][19][20][21][22][23][24]). …”

Section: Jhep11(2010)116mentioning

confidence: 99%

Higher spin interactions with scalar matter on constant curvature spacetimes: conserved current and cubic coupling generating functions

Bekaert

Meunier

2010

“…There are certain technical difficulties, though, in extending the applicability of the BRST deformation scheme to spaces of constant curvature. One may use the ambient-space formulation [49][50][51] for AdS space, in particular, to avoid these issues. Then one could construct covariant higher-spin vertices in AdS, and the results could be compared with those…”

Section: Jhep01(2014)087mentioning

confidence: 99%

Gravitational interactions of higher-spin fermions

Henneaux

Gómez

Rahman

2014

Abstract:We investigate the cubic interactions of a massless higher-spin fermion with gravity in flat space and present covariant 2 − s − s vertices, compatible with the gauge symmetries of the system, preserving parity. This explicit construction relies on the BRST deformation scheme that assumes locality and Poincaré invariance. Consistent nontrivial cubic deformations exclude minimal gravitational coupling and may appear only with a number of derivatives constrained in a given range. Derived in an independent manner, our results do agree with those obtained from the light-cone formulation or inspired by string theory. We also show that none of the Abelian vertices deform the gauge transformations, while all the non-Abelian ones are obstructed in a local theory beyond the cubic order.

“…The reason behind this difference with respect to the case of flat background is that massless fields in (A)dS have mass-like terms depending on the spin, so that the various propagating components in ϕ actually satisfy different equations of motion. However, the effective particle content associated to the Lagrangian (2.62) can be identified comparing with the unconstrained Lagrangian for (A)dS triplets of [35,38,55]. In that context the relevant equations after eliminating an auxiliary field are…”

Section: Symmetric Tensorsmentioning

confidence: 99%

Maxwell-like Lagrangians for higher spins

Campoleoni

Francia

2013

122

We show how implementing invariance under divergence-free gauge transformations leads to a remarkably simple Lagrangian description of massless bosons of any spin. Our construction covers both flat and (A)dS backgrounds and extends to tensors of arbitrary mixed-symmetry type. Irreducible and traceless fields produce single-particle actions, while whenever trace constraints can be dispensed with the resulting Lagrangians display the same reducible, multi-particle spectra as those emerging from the tensionless limit of free open-string field theory. For all explored options the corresponding kinetic operators take essentially the same form as in the spin-one, Maxwell case.