8 research outputs found
Higher Spin Fields in Siegel Space, Currents and Theta Functions
Dynamics of four-dimensional massless fields of all spins is formulated in
the Siegel space of complex symmetric matrices. It is shown that
the unfolded equations of free massless fields, that have a form of
multidimensional Schrodinger equations, naturally distinguish between positive-
and negative-frequency solutions of relativistic field equations, i.e.
particles and antiparticles. Multidimensional Riemann theta functions are shown
to solve massless field equations in the Siegel space. We establish the
correspondence between conserved higher-spin currents in four-dimensional
Minkowski space and those in the ten-dimensional matrix space. It is shown that
global symmetry parameters of the current in the matrix space should be
singular to reproduce a nonzero current in Minkowski space. The \D-function
integral evolution formulae for 4d massless fields in the Fock-Siegel space are
obtained. The generalization of the proposed scheme to higher dimensions and
systems of higher ranks is considered.Comment: LaTeX, 38 pages, v.3: clarifications, acknowledgements and references
added, typos corrected, v.4: more comments and references added, typos
corrected, the version to appear in JHE
Superfield Theories in Tensorial Superspaces and the Dynamics of Higher Spin Fields
We present the superfield generalization of free higher spin equations in
tensorial superspaces and analyze tensorial supergravities with GL(n) and SL(n)
holonomy as a possible framework for the construction of a non-linear higher
spin field theory. Surprisingly enough, we find that the most general solution
of the supergravity constraints is given by a class of superconformally flat
and OSp(1|n)-related geometries. Because of the conformal symmetry of the
supergravity constraints and of the higher spin field equations such geometries
turn out to be trivial in the sense that they cannot generate a `minimal'
coupling of higher spin fields to their potentials even in curved backgrounds
with a non-zero cosmological constant. This suggests that the construction of
interacting higher spin theories in this framework might require an extension
of the tensorial superspace with additional coordinates such as twistor-like
spinor variables which are used to construct the OSp(1|2n) invariant
(`preonic') superparticle action in tensorial superspace.Comment: LaTeX, 30 pages, no figures. V2. Discussion on conventional
constraints extended, typos corrected, JHEP style, to appear in JHE
Higher-Spin Gauge Fields Interacting with Scalars: The Lagrangian Cubic Vertex
We apply a recently presented BRST procedure to construct the Largangian
cubic vertex of higher-spin gauge field triplets interacting with massive free
scalars. In flat space, the spin-s triplet propagates the series of irreducible
spin-s, s-2,..,0/1 modes which couple independently to corresponding conserved
currents constructed from the scalars. The simple covariantization of the flat
space result is not enough in AdS, as new interaction vertices appear. We
present in detail the cases of spin-2 and spin-3 triplets coupled to scalars.
Restricting to a single irreducible spin-s mode we uncover previously obtained
results. We also present an alternative derivation of the lower spin results
based on the idea that higher-spin gauge fields arise from the gauging of
higher derivative symmetries of free matter Lagrangians. Our results can be
readily applied to holographic studies of higher-spin gauge theories.Comment: 26 pages, v2: references adde
Dynamics of Higher Spin Fields and Tensorial Space
The structure and the dynamics of massless higher spin fields in various
dimensions are reviewed with an emphasis on conformally invariant higher spin
fields. We show that in D=3,4,6 and 10 dimensional space-time the conformal
higher spin fields constitute the quantum spectrum of a twistor-like particle
propagating in tensorial spaces of corresponding dimensions. We give a detailed
analysis of the field equations of the model and establish their relation with
known formulations of free higher spin field theory.Comment: JHEP3 style, 40 pages; v2 typos corrected, comments and references
added; v3 published versio
Conserved higher-spin charges in AdS4
Gauge invariant conserved conformal currents built from massless fields of all spins in 4d Minkowski space–time and AdS4 are described in the unfolded dynamics approach. The current cohomology associated with non-zero conserved charges is found. The resulting list of charges is shown to match the space of parameters of the conformal higher-spin symmetry algebra in four dimensions