430 research outputs found
Gauge fields in (anti)-de Sitter space and Connections of its symmetry algebra
The generalized connections of the (anti)-de Sitter space symmetry algebra,
which are differential forms of arbitrary degree with values in any irreducible
(spin)-tensor representation of the (anti)-de Sitter algebra, are studied. It
is shown that arbitrary-spin gauge field in (anti)-de Sitter space, massless or
partially-massless, can be described by a single connection. A 'one-to-one'
correspondence between the connections of the (anti)-de Sitter algebra and the
gauge fields is established. The gauge symmetry is manifest and auxiliary
fields are automatically included in the formalism.Comment: 37 pages; comments on p.24-25 are extended; references adde
Mixed-Symmetry Massless Fields in Minkowski space Unfolded
The unfolded formulation for arbitrary massless mixed-symmetry bosonic and
fermionic fields in Minkowski space is constructed. The unfolded form is proved
to be uniquely determined by the requirement that all gauge symmetries are
manifest. The unfolded equations have the form of a covariant constancy
condition. The gauge fields and gauge parameters are differential forms with
values in certain irreducible Lorentz tensors. The unfolded equations for
bosons determine completely those for fermions. The proposed unfolded
formulation also contains dual formulations for massless mixed-symmetry fields.Comment: 59 pages; PDOF counting added; typos correcte
On Locality, Holography and Unfolding
We study the functional class and locality problems in the context of
higher-spin theories and Vasiliev's equations. A locality criterion that is
sufficient to make higher-spin theories well-defined as field theories on
Anti-de-Sitter space is proposed. This criterion identifies admissible
pseudo-local field redefinitions which preserve AdS/CFT correlation functions
as we check in the 3d example. Implications of this analysis for known
higher-spin theories are discussed. We also check that the cubic coupling
coefficients previously fixed in 3d at the action level give the correct CFT
correlation functions upon computing the corresponding Witten diagrams.Comment: 36 pages, LaTex. References added, typos corrected. Final version to
appear in JHE
Formal Higher-Spin Theories and Kontsevich-Shoikhet-Tsygan Formality
The formal algebraic structures that govern higher-spin theories within the
unfolded approach turn out to be related to an extension of the Kontsevich
Formality, namely, the Shoikhet-Tsygan Formality. Effectively, this allows one
to construct the Hochschild cocycles of higher-spin algebras that make the
interaction vertices. As an application of these results we construct a family
of Vasiliev-like equations that generate the Hochschild cocycles with
symmetry from the corresponding cycles. A particular case of may be
relevant for the on-shell action of the theory. We also give the exact
equations that describe propagation of higher-spin fields on a background of
their own. The consistency of formal higher-spin theories turns out to have a
purely geometric interpretation: there exists a certain symplectic invariant
associated to cutting a polytope into simplices, namely, the Alexander-Spanier
cocycle.Comment: typos fixed, many comments added, 36 pages + 20 pages of Appendices,
3 figure
Correlation Functions of Sp(2n) Invariant Higher-Spin Systems
We study the general structure of correlation functions in an
Sp(2n)-invariant formulation of systems of an infinite number of higher-spin
fields. For n=4,8 and 16 these systems comprise the conformal higher-spin
fields in space-time dimensions D=4,6 and 10, respectively, while when n=2, one
deals with conventional D=3 conformal field theories of scalars and spinors. We
show that for n>2 the Sp(2n) symmetry and current conservation makes the
3-point correlators of two (rank-one or rank-two) conserved currents with a
scalar operator be that of free theory.This situation is analogous to the one
in conventional conformal field theories, where conservation of higher-spin
currents implies that the theories are free.Comment: 26 pages, some clarifications added, published versio
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