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

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

Supersymmetric Higher Spin Theories

We revisit the higher spin extensions of the anti de Sitter algebra in four dimensions that incorporate internal symmetries and admit representations that contain fermions, classified long ago by Konstein and Vasiliev. We construct the $dS_4$, Euclidean and Kleinian version of these algebras, as well as the corresponding fully nonlinear Vasiliev type higher spin theories, in which the reality conditions we impose on the master fields play a crucial role. The ${\cal N}=2$ supersymmetric higher spin theory in $dS_4$, on which we elaborate further, is included in this class of models. A subset of Konstein-Vasiliev algebras are the higher spin extensions of the $AdS_4$ superalgebras $osp(4|{\cal N})$ for ${\cal N}=1,2,4$ mod 4 and can be realized using fermionic oscillators. We tensor the higher superalgebras of the latter kind with appropriate internal symmetry groups and show that the ${\cal N}=3$ mod 4 higher spin algebras are isomorphic to those with ${\cal N}=4$ mod 4. We describe the fully nonlinear higher spin theories based on these algebras as well, and we elaborate further on the ${\cal N}=6$ supersymmetric theory, providing two equivalent descriptions one of which exhibits manifestly its relation to the ${\cal N}=8$ supersymmetric higher spin theory.Comment: 30 pages. Contribution to J. Phys. A special volume on "Higher Spin Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasilie

Codimension One Branes

We study codimension one branes, i.e. p-branes in (p+2)-dimensions, in the superembedding approach for the cases where the worldvolume superspace is embedded in a minimal target superspace with half supersymmetry breaking. This singles out the cases p=1,2,3,5,9. For p=3,5,9 the superembedding geometry naturally involves a fundamental super 2-form potential on the worldvolume whose generalised field strength obeys a constraint deducible from considering an open supermembrane ending on the p-brane. This constraint, together with the embedding constraint, puts the system on-shell for p=5 but overconstrains the 9-brane in D=11 such that the Goldstone superfield is frozen. For p=3 these two constraints give rise to an off-shell linear multiplet on the worldvolume. An alternative formulation of this case is given in which the linear multiplet is dualised to an off-shell scalar multiplet. Actions are constructed for both cases and are shown to give equivalent equations of motion. After gauge fixing a local Sp(1) symmetry associated with shifts in the Sp(1)_R Goldstone modes, we find that the auxiliary fields in the scalar multiplet parametrise a two-sphere. For completeness we also discuss briefly the cases p=1,2 where the equations of motion (for off-shell multiplets) are obtained from an action principle.Comment: 38 pages, latex, cover page correcte

Correlation Functions in ω\omega-Deformed N=6 Supergravity

Gauged N=8 supergravity in four dimensions is now known to admit a deformation characterized by a real parameter $\omega$ lying in the interval $0\le\omega\le \pi/8$. We analyse the fluctuations about its anti-de Sitter vacuum, and show that the full N=8 supersymmetry can be maintained by the boundary conditions only for $\omega=0$. For non-vanishing $\omega$, and requiring that there be no propagating spin s>1 fields on the boundary, we show that N=3 is the maximum degree of supersymmetry that can be preserved by the boundary conditions. We then construct in detail the consistent truncation of the N=8 theory to give $\omega$-deformed SO(6) gauged N=6 supergravity, again with $\omega$ in the range $0\le\omega\le \pi/8$. We show that this theory admits fully N=6 supersymmetry-preserving boundary conditions not only for $\omega=0$, but also for $\omega=\pi/8$. These two theories are related by a U(1) electric-magnetic duality. We observe that the only three-point functions that depend on $\omega$ involve the coupling of an SO(6) gauge field with the U(1) gauge field and a scalar or pseudo-scalar field. We compute these correlation functions and compare them with those of the undeformed N=6 theory. We find that the correlation functions in the $\omega=\pi/8$ theory holographically correspond to amplitudes in the U(N)_k x U(N)_{-k} ABJM model in which the U(1) Noether current is replaced by a dynamical U(1) gauge field. We also show that the $\omega$-deformed N=6 gauged supergravities can be obtained via consistent reductions from the eleven-dimensional or ten-dimensional type IIA supergravities.Comment: 38 pages, one figur