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Register a new userBoundary values of mixed-symmetry massless fields in AdS space
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We elaborate on the ambient space approach to boundary values of $AdS_{d+1}$ gauge fields and apply it to massless fields of mixed-symmetry type. In the most interesting case of odd-dimensional bulk the respective leading boundary values are conformal gauge fields subject to the invariant equations. Our approach gives a manifestly conformal and gauge covariant formulation for these fields. Although such formulation employs numerous auxiliary fields, it comes with a systematic procedure for their elimination that results in a more concise formulation involving only a reasonable set of auxiliaries, which eventually (at least in principle) can be reduced to the minimal formulation in terms of the irreducible Lorentz tensors. The simplest mixed-symmetry field, namely, the rank-3 tensor associated to the two-row Young diagram, is considered in some details.
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We formulate Fradkin-Vasiliev type theory of massless higher spin fields in AdS(5). The corresponding action functional describes cubic order approximation to gravitational interactions of bosonic mixed-symmetry fields of a particular hook symmetry type and totally symmetric bosonic and fermionic fields.
Under the hypotheses of analyticity, locality, Lorentz covariance, and Poincare invariance of the deformations, combined with the requirement that the interaction vertices contain at most two spatiotemporal derivatives of the fields, we investigate the consistent selfinteractions that can be added to a collection of massless tensor fields with the mixed symmetry (3,1) and respectively (2,2). The computations are done with the help of the deformation theory based on a cohomological approach, in the context of the antifield-BRST formalism. Our result is that no selfinteractions that deform the original gauge transformations emerge. In the case of the collection of (2,2) tensor fields it is possible to add a sum of cosmological terms to the free Lagrangian.
We construct a concise gauge invariant formulation for massless, partially massless, and massive bosonic AdS fields of arbitrary symmetry type at the level of equations of motion. Our formulation admits two equivalent descriptions: in terms of the ambient space and in terms of an appropriate vector bundle, as an explicitly local first-order BRST formalism. The second version is a parent-like formulation that can be used to generate various other formulations via equivalent reductions. In particular, we demonstrate a relation to the unfolded description of massless and partially massless fields.
We rederive the characters of all unitary irreducible representations of the $(d+1)$-dimensional de Sitter spacetime isometry algebra $mathfrak{so}(1,d+1)$, and propose a dictionary between those representations and massive or (partially) massless fields on de Sitter spacetime. We propose a way of taking the flat limit of representations in (anti-) de Sitter spaces in terms of these characters, and conjecture the spectrum resulting from taking the flat limit of mixed-symmetry fields in de Sitter spacetime. We comment on a possible equivalent of the scalar singleton for the de Sitter (dS) spacetime.
We study the properties of nonlinear superalgebras $mathcal{A}$ and algebras $mathcal{A}_b$ arising from a one-to-one correspondence between the sets of relations that extract AdS-group irreducible representations $D(E_0,s_1,s_2)$ in AdS$_d$-spaces and the sets of operators that form $mathcal{A}$ and $mathcal{A}_b$, respectively, for fermionic, $s_i=n_i+{1/2}$, and bosonic, $s_i=n_i$, $n_i in mathbb{N}_0$, $i=1,2$, HS fields characterized by a Young tableaux with two rows. We consider a method of constructing the Verma modules $V_mathcal{A}$, $V_{mathcal{A}_b}$ for $mathcal{A}$, $mathcal{A}_b$ and establish a possibility of their Fock-space realizations in terms of formal power series in oscillator operators which serve to realize an additive conversion of the above (super)algebra ($mathcal{A}$) $mathcal{A}_b$, containing a set of 2nd-class constraints, into a converted (super)algebra $mathcal{A}_{b{}c}$ = $mathcal{A}_{b}$ + $mathcal{A}_b$ ($mathcal{A}_c$ = $mathcal{A}$ + $mathcal{A}$), containing a set of 1st-class constraints only. For the algebra $mathcal{A}_{b{}c}$, we construct an exact nilpotent BFV--BRST operator $Q$ having nonvanishing terms of 3rd degree in the powers of ghost coordinates and use $Q$ to construct a gauge-invariant Lagrangian formulation (LF) for HS fields with a given mass $m$ (energy $E_0(m)$) and generalized spin $mathbf{s}$=$(s_1,s_2)$. LFs with off-shell algebraic constraints are examined as well.
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