Conformal coupling of higher spin gauge fields to a scalar field in AdS4 and generalized Weyl invariance

Abstract

The higher spin interaction currents for the conformally coupled scalar in AdS 4 space for both regular and irregular boundary condition corresponding to the free and interacting critical point of the boundary O(N) sigma model are constructed. The explicit form of the linearized interaction of the scalar and spin two and four gauge fields in the AdS D space using Noether's procedure for the corresponding spin two and four linearized gauge and generalized Weyl transformations are obtained.

Unfolded equations for current interactions of 4d massless fields as a free system in mixed dimensions

“…The unfolded machinery makes is technically as simple as that in Minkowski case. This should be compared to other approaches to the analysis of HS conserved currents in AdS background [34,35,36,37]. (Note that the case of AdS 3 was considered in [38,39]).…”

Effective action in a higher-spin background

“…Various explicit sets of conformal conserved currents on maximally symmetric spacetimes were also provided in [34,35,[44][45][46][47][50][51][52][53].…”

“…From equations (3.4) and (3.12) we see that the finite part of the effective action receives contributions only from non-negative powers of t in K[g|t]: 50) that is, from the HKE coefficients a n [g] with n d/2. In fact, for d > 2, it is more convenient to first replace K[g|t] in (3.4) by…”

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

“…minimal) cubic couplings between a complex scalar matter field and a collection of higher-spin tensor gauge fields have already been investigated in the metriclike formulation on Minkowski [4][5][6][7] and anti de Sitter [7][8][9][10] spacetimes (see also the recent work [11] in the frame-like formulation). The Noether cubic interaction between a complex scalar field and a tensor gauge field takes place through a symmetric current, quadratic in the scalar field and conserved at linearized level.…”

“…the singleton) was considered in [8,9] and AdS 3 was the background spacetime in [35,36]; secondly, the explicit expression of the currents is known at all orders in the scalar curvature, while only the first order correction to the flat expression was provided in [8,9]; thirdly, the currents (4.2) are conserved on-shell in the usual sense of (2.1) while the ones of [7] obey to the weaker conservation law introduced by Fronsdal [14]. Of course, strictly speaking the third comment should not be understood as a loss of generality in the previous results of [7,10].…”