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

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

Higher Spin N=8 Supergravity

The product of two N=8 supersingletons yields an infinite tower of massless states of higher spin in four dimensional anti de Sitter space. All the states with spin s > 1/2 correspond to generators of Vasiliev's super higher spin algebra shs^E (8|4) which contains the D=4, N=8 anti de Sitter superalgebra OSp(8|4). Gauging the higher spin algebra and introducing a matter multiplet in a quasi-adjoint representation leads to a consistent and fully nonlinear equations of motion as shown sometime ago by Vasiliev. We show the embedding of the N=8 AdS supergravity equations of motion in the full system at the linearized level and discuss the implications for the embedding of the interacting theory. We furthermore speculate that the boundary N=8 singleton field theory yields the dynamics of the N=8 AdS supergravity in the bulk, including all higher spin massless fields, in an unbroken phase of M-theory.Comment: 64 pages, latex, considerably expanded version, submitted for publicatio

Towards Massless Higher Spin Extension of D=5, N=8 Gauged Supergravity

The AdS_5 superalgebra PSU(2,2|4) has an infinite dimensional extension, which we denote by hs(2,2|4). We show that the gauging of hs(2,2|4) gives rise to a spectrum of physical massless fields which coincides with the symmetric tensor product of two AdS_5 spin-1 doubletons (i.e. the N=4 SYM multiplets living on the boundary of AdS_5). This product decomposes into levels \ell=0,1,2,..,\infty of massless supermultiplets of PSU(2,2|4). In particular, the D=5, N=8 supergravity multiplet arises at level \ell=0. In addition to a master gauge field, we construct a master scalar field containing the s=0,1/2 fields, the anti-symmetric tensor field of the gauged supergravity and its higher spin analogs. We define the linearized constraints and obtain the linearized field equations of the full spectrum, including those of D=5,N=8 gauged supergravity and in particular the self-duality equations for the 2-form potentials of the gauged supergravity (forming a 6-plet of SU(4)), and their higher spin cousins with s=2,3,...,\infty.Comment: 36 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

Symmetries of P-Branes

Using canonical methods, we study the invariance properties of a bosonic $p$--brane propagating in a curved background locally diffeomorphic to $M\times G$, where $M$ is spacetime and $G$ a group manifold. The action is that of a gauged sigma model in $p+1$ dimensions coupled to a Yang--Mills field and a $(p+1)$--form in $M$. We construct the generators of Yang-Mills and tensor gauge transformations and exhibit the role of the $(p+1)$--form in cancelling the potential Schwinger terms. We also discuss the Noether currents associated with the global symmetries of the action and the question of the existence of infinite dimensional symmetry algebras, analogous to the Kac-Moody symmetry of the string.Comment: 15 pages, CTP-TAMU-32/92, SISSA 182/92/E