General trilinear interaction for arbitrary even higher spin gauge fields

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.

“…[37,38], while, in metric-like approach, in refs. [39][40][41]. In BRST approach, cubic vertices involving arbitrary spin massless and massive fields were derived in ref.…”

Section: Jhep11(2017)197mentioning

confidence: 99%

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

Metsaev

2017

“…The number of derivatives in these vertices, as the light-cone formulation elucidates, is restricted, which provides a way of classifying them [8,9]. The complete list of such vertices for bosonic fields appeared already in [10,11], but their explicit construction may call for the Noether procedure [12][13][14] or the BRST-BV cohomological methods [6,7,15,16]. The tensionless limit of open string theory, on the other hand, yields a set of cubic vertices in one-to-one correspondence with that found in the light-cone formulation [17,18].…”

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 picture that emerges is a general consensus on the overall structure of the cubic interactions. The results have been derived using different formalistic apparatuses: (i) field theoretic Noether-coupling/BRST methods (see for instance [38][39][40]) generalizing the approach of the 1984 work of Berends, Burgers and vanDam [19], (ii) limits of the Vasiliev theory (see for instance [41,42]) cubic interactions [20], (iii) limits of string amplitudes [21,43], (iv) string field theory (see for instance [44][45][46]) inspired BRST-methods [9,47,48] in the spirit of the present author's 1988 paper [16], (v) FDA-L ∞ -methods [8], (vi) generating function Noether methods [49,50] generalizing BBvD [7,36,37], and finally (vii) light-front methods by Metsaev [1,2,6] extending the original results of [4,5,35].…”

Section: Relation To Current Research On Minkowski Space Interactionsmentioning

confidence: 92%

A Riccati type PDE for light-front higher helicity vertices

Bengtsson

2014

This paper is based on a curious observation about an equation related to the tracelessness constraints of higher spin gauge fields. A similar equation also occurs in the theory of continuous spin representations of the Poincaré group. Expressed in an oscillator basis for the higher spin fields, the equation becomes a non-linear partial differential operator of the Riccati type acting on the vertex functions. The consequences of the equation for the cubic vertex is investigated in the light-front formulation of higher spin theory. The vertex is fixed by the PDE up to a set of terms that can be considered as boundary data for the PDE. These terms can serve as off-shell quantum corrections.In order to set the present work in perspective, some comments and comparisons to recent research on higher spin interactions are made. A few particular cubic vertices are calculated explicitly and compared to similar results in the literature, in particular the interesting cases 2 − 3 − 3 and 3 − 2 − 2 involving spin 2 fields.