Higher spin gauge theories in any dimension

Abstract

Some general properties of higher spin gauge theories are summarized with the emphasize on the nonlinear theories in any dimension.

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

“…For the so-called "triplet" arising from the open string leading Regge trajectory [46,47,[49][50][51][52][53] (see also [10,23]), the situation is more subtle: although traceful conserved currents can indeed source the symmetric tensor field, only the traceless component of the currents studied here leads to genuine minimal interactions. 2 The kth trace of the current of rank r is a current of rank r − 2k (lower than r) and contains r derivatives. However, any non-trivial rank-s conserved current built from a scalar field is known to contain up to s derivatives.…”

“…The Lie (sub)algebra of such symbols is the off-shell higher-spin algebra of Vasiliev (see e.g. [1][2][3] for reviews).…”

“…The quotient of the Vasiliev off-shell algebra by the corresponding two-sided ideal (spanned by elements that are sum of elements proportional to a sp(2)-constraint) is the Vasiliev on-shell higher-spin algebra (see e.g. [1][2][3] for more details). The situation is somewhat different for the massive scalar field module spanned by the harmonic homogeneous functions on the ambient space of subsection 3.4, because this module is not annihilated by the operators corresponding to X 2 and X ·P (see e.g.…”

“…It is very tempting to conjecture that the full action (2.13) should be interpreted as arising from the gauging of the rigid symmetries of the free scalar matter field, which generalize the U(1) and isometries of (A)dS d , so that the local symmetries (5.14) generalize the local U(1) and diffeomorphisms (see [5][6][7]30] and refs therein for more comments on this point of view). In any case, the unfolded equations (on-shell [1][2][3] and off-shell [39, 40]) JHEP11 (2010)116 precisely arise from the gauging of the same rigid algebra of (on/off shell) symmetries but the scalar field is included in the gauge field multiplet.…”

“…Although a higherspin generalization of gravity is available through the frame-like formulation of Vasiliev (see e.g. [1][2][3] for some reviews) extending the Cartan-Weyl formulation of general relativity, the first principles analogous to the parallel transport and to the local affine covariance on the geometrical side, or to the gauge and equivalence principles on the physical side, still remain mysterious. The latter physical principles, underlying the low-spin interactions, are best displayed in the minimal couplings between matter and gauge fields, so higher-spin generalizations thereof might be a proper place to look for inspiration.…”