7,946 research outputs found
An Exact Solution of 4D Higher-Spin Gauge Theory
We give a one-parameter family of exact solutions to four-dimensional
higher-spin gauge theory invariant under a deformed higher-spin extension of
SO(3,1) and parameterized by a zero-form invariant. All higher-spin gauge
fields vanish, while the metric interpolates between two asymptotically AdS4
regions via a dS3-foliated domainwall and two H3-foliated Robertson-Walker
spacetimes -- one in the future and one in the past -- with the scalar field
playing the role of foliation parameter. All Weyl tensors vanish, including
that of spin two. We furthermore discuss methods for constructing solutions,
including deformation of solutions to pure AdS gravity, the gauge-function
approach, the perturbative treatment of (pseudo-)singular initial data
describing isometric or otherwise projected solutions, and zero-form
invariants.Comment: 47 pages. v3: global properties of the solution clarified, minor
corrections made, discussion and refs revise
7D Bosonic Higher Spin Theory: Symmetry Algebra and Linearized Constraints
We construct the minimal bosonic higher spin extension of the 7D AdS algebra
SO(6,2), which we call hs(8*). The generators, which have spin s=1,3,5,..., are
realized as monomials in Grassmann even spinor oscillators. Irreducibility, in
the form of tracelessness, is achieved by modding out an infinite dimensional
ideal containing the traces. In this a key role is played by the tree bilinear
traces which form an SU(2)_K algebra. We show that gauging of hs(8*) yields a
spectrum of physical fields with spin s=0,2,4,...which make up a UIR of hs(8*)
isomorphic to the symmetric tensor product of two 6D scalar doubletons. The
scalar doubleton is the unique SU(2)_K invariant 6D doubleton. The spin s\geq 2
sector comes from an hs(8*)-valued one-form which also contains the auxiliary
gauge fields required for writing the curvature constraints in covariant form.
The physical spin s=0 field arises in a separate zero-form in a `quasi-adjoint'
representation of hs(8*). This zero-form also contains the spin s\geq 2 Weyl
tensors, i.e. the curvatures which are non-vanishing on-shell. We suggest that
the hs(8*) gauge theory describes the minimal bosonic, massless truncation of M
theory on AdS_7\times S^4 in an unbroken phase where the holographic dual is
given by N free (2,0) tensor multiplets for large N.Comment: 23 pages, late
Superspace Formulation of 4D Higher Spin Gauge Theory
Interacting AdS_4 higher spin gauge theories with N \geq 1 supersymmetry so
far have been formulated as constrained systems of differential forms living in
a twistor extension of 4D spacetime. Here we formulate the minimal N=1 theory
in superspace, leaving the internal twistor space intact. Remarkably, the
superspace constraints have the same form as those defining the theory in
ordinary spacetime. This construction generalizes straightforwardly to higher
spin gauge theories N>1 supersymmetry.Comment: 24 p
Real Forms of Complex Higher Spin Field Equations and New Exact Solutions
We formulate four dimensional higher spin gauge theories in spacetimes with
signature (4-p,p) and nonvanishing cosmological constant. Among them are chiral
models in Euclidean (4,0) and Kleinian (2,2) signature involving half-flat
gauge fields. Apart from the maximally symmetric solutions, including de Sitter
spacetime, we find: (a) SO(4-p,p) invariant deformations, depending on a
continuous and infinitely many discrete parameters, including a degenerate
metric of rank one; (b) non-maximally symmetric solutions with vanishing Weyl
tensors and higher spin gauge fields, that differ from the maximally symmetric
solutions in the auxiliary field sector; and (c) solutions of the chiral models
furnishing higher spin generalizations of Type D gravitational instantons, with
an infinite tower of Weyl tensors proportional to totally symmetric products of
two principal spinors. These are apparently the first exact 4D solutions with
non-vanishing massless higher spin fields.Comment: 40 pages, late
Scalar Field Corrections to AdS_4 Gravity from Higher Spin Gauge Theory
We compute the complete contribution to the stress-energy tensor in the
minimal bosonic higher spin theory in D=4 that is quadratic in the scalar
field. We find arbitrarily high derivative terms, and that the total sign of
the stress-energy tensor depends on the parity of the scalar field.Comment: 15 pages + appendix (30 pages
Analysis of Higher Spin Field Equations in Four Dimensions
The minimal bosonic higher spin gauge theory in four dimensions contains
massless particles of spin s=0,2,4,.. that arise in the symmetric product of
two spin 0 singletons. It is based on an infinite dimensional extension of the
AdS_4 algebra a la Vasiliev. We derive an expansion scheme in which the
gravitational gauge fields are treated exactly and the gravitational curvatures
and the higher spin gauge fields as weak perturbations. We also give the
details of an explicit iteration procedure for obtaining the field equations to
arbitrary order in curvatures. In particular, we highlight the structure of all
the quadratic terms in the field equations.Comment: Latex, 30 pages, several clarifications and few references adde
Spectrum of D=6, N=4b Supergravity on AdS_3 x S^3
The complete spectrum of D=6, N=4b supergravity with n tensor multiplets
compactified on AdS_3 x S^3 is determined. The D=6 theory obtained from the K_3
compactification of Type IIB string requires that n=21, but we let n be
arbitrary. The superalgebra that underlies the symmetry of the resulting
supergravity theory in AdS_3 coupled to matter is SU(1,1|2)_L x SU(1,1|2)_R.
The theory also has an unbroken global SO(4)_R x SO(n) symmetry inherited from
D=6. The spectrum of states arranges itself into a tower of spin-2
supermultiplets, a tower of spin-1, SO(n) singlet supermultiplets, a tower of
spin-1 supermultiplets in the vector representation of SO(n) and a special
spin-1/2 supermultiplet also in the vector representation of SO(n). The SU(2)_L
x SU(2)_R Yang-Mills states reside in the second level of the spin-2 tower and
the lowest level of the spin-1, SO(n) singlet tower and the associated field
theory exhibits interesting properties.Comment: 37 pages, latex, 5 tables and 3 figures, typos corrected, a reference
adde
Holography in 4D (Super) Higher Spin Theories and a Test via Cubic Scalar Couplings
The correspondences proposed previously between higher spin gauge theories
and free singleton field theories were recently extended into a more complete
picture by Klebanov and Polyakov in the case of the minimal bosonic theory in
D=4 to include the strongly coupled fixed point of the 3d O(N) vector model.
Here we propose an N=1 supersymmetric version of this picture. We also
elaborate on the role of parity in constraining the bulk interactions, and in
distinguishing two minimal bosonic models obtained as two different consistent
truncations of the minimal N=1 model that retain the scalar or the
pseudo-scalar field. We refer to these models as the Type A and Type B models,
respectively, and conjecture that the latter is holographically dual to the 3d
Gross-Neveu model. In the case of the Type A model, we show the vanishing of
the three-scalar amplitude with regular boundary conditions. This agrees with
the O(N) vector model computation of Petkou, thereby providing a non-trivial
test of the Klebanov-Polyakov conjecture.Comment: 30p
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