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

XI. Researches on spectrum analysis

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An action principle for Vasiliev's four-dimensional higher-spin gravity

We provide Vasiliev's fully nonlinear equations of motion for bosonic gauge fields in four spacetime dimensions with an action principle. We first extend Vasiliev's original system with differential forms in degrees higher than one. We then derive the resulting duality-extended equations of motion from a variational principle based on a generalized Hamiltonian sigma-model action. The generalized Hamiltonian contains two types of interaction freedoms: One set of functions that appears in the Q-structure of the generalized curvatures of the odd forms in the duality-extended system; and another set depending on the Lagrange multipliers, encoding a generalized Poisson structure, i.e. a set of polyvector fields of ranks two or higher in target space. We find that at least one of the two sets of interaction-freedom functions must be linear in order to ensure gauge invariance. We discuss consistent truncations to the minimal Type A and B models (with only even spins), spectral flows on-shell and provide boundary conditions on fields and gauge parameters that are compatible with the variational principle and that make the duality-extended system equivalent, on shell, to Vasiliev's original system.Comment: 37 pages. References added, corrected typo

The Hydrogendifluoride Anion in an Asymmetric Crystalline Environment: The Crystal and Molecular Structure of Trithioureatellurium(II) Di(Hydrogendifluoride)

The crystal structure of Te[CS(NH2l2h(FHF)2, I , was determined at 133K using single crystal x-ray diffraction techniques. A total of 6042 independent reflections were observed for the monoclinic crystals (space group P21/c, No. 14, a = 0.5846(3), b = 2.046(1), c = 1.1433(7) nm, (J = 94.69(5) 0 , Ve= 1.363(1) nm3, (Z = 4), in the range 4.0° s 219 s 70.0° of which 5243 had F0 2 > 3a (F0 2). The trithiourea- tellurium (II) molecules crystallize as dimeric distorted square planar cations [Te(tu)3]24+ (tu = thiourea) located about an inversion center. The cations are linked by N-H ... F hydrogen bonds. The environment about the two independent (FHFt anions is decidedly asymmetric and therefore the hydrogen atoms are not centered between the fluorine atoms

How higher-spin gravity surpasses the spin two barrier: no-go theorems versus yes-go examples

Aiming at non-experts, we explain the key mechanisms of higher-spin extensions of ordinary gravity. We first overview various no-go theorems for low-energy scattering of massless particles in flat spacetime. In doing so we dress a dictionary between the S-matrix and the Lagrangian approaches, exhibiting their relative advantages and weaknesses, after which we high-light potential loop-holes for non-trivial massless dynamics. We then review positive yes-go results for non-abelian cubic higher-derivative vertices in constantly curved backgrounds. Finally we outline how higher-spin symmetry can be reconciled with the equivalence principle in the presence of a cosmological constant leading to the Fradkin--Vasiliev vertices and Vasiliev's higher-spin gravity with its double perturbative expansion (in terms of numbers of fields and derivatives).Comment: LaTeX, 50 pages, minor changes, many refs added; version accepted for publication in Reviews of Modern Physic

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

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