Higher Spin Fields in Hyperspace. A Review

Abstract

Abstract:We give an introduction to the so-called tensorial, matrix or hyperspace approach to the description of massless higher-spin fields.

From Coxeter higher-spin theories to strings and tensor models

“…The point is that, as emphasized in [123,124], the multi-particle states of a lower-dimensional model can be identified with elementary states in an appropriate higherdimensional theory. Such interpretation turns out to be most natural within the matrixspace approach to massless field theories elaborated in [125,114,126,127] (see also [92] and recent reviews [128,129]). Moreover, the maximal space-time where such models admit interpretation in terms of local fields is ten-dimensional [125,126,127] which is just the superstring space-time dimension.…”

“…In fact this is a simplest manifestation of the fact discussed in the beginning of Section 6.2 that tensoring of the lower-dimensional models can give higherdimensional ones. Though this phenomenon is less straightforward for the higher tensor products since higher-dimensional Lorentz algebras are not real forms of the direct sums of a number of sl 2 (C) the results of [125]- [129] suggest that a proper interpretation can be available in a certain limit in which the contribution of (delocalized) branes associated with the lower rank (dimensional) models can be discarded. In this model, the lower-rank states start with ω and C that depend either only on y a n ,k a n or only onȳ a n ,k a n .…”

Supersymmetric continuous spin gauge theory

“…Let us mention that there is a different formulation in which similar infinite sets of higher spin fields appear. In this formulation the infinite sets of higher spin fields are described as scalar and spinor fields in the so-called tensorial (or hyper) spaces (for a review and references see [62]). Supersymmetric higher spin models constructed in hyperspace [63][64][65][66] describe infinite-dimensional higher spin supermultiplets and thus differ from the conventional higher spin supermultiplets obtained in the helicity limit of the supersymmetric CSPs.…”

Conformal geometry and (super)conformal higher-spin gauge theories

“…The structure of the (super) CHS actions presented in this paper indicate that there should exist a generating formalism to formulate all of these models in terms of a single hyper-action. Recently there has been much interest in the so-called tensorial or hyperspace approach to the description of massless higher-spin (super)fields [104][105][106][107][108][109][110][111][112][113][114][115][116][117][118], see also [119] for a pedagogical review. It would be interesting to study whether the conformal (super)space methods can be extended to hyperspace.…”