Higher-Spin Theory and Space-Time Metamorphoses

Introductory lectures on higher-spin gauge theory given at 7 Aegean workshop on non-Einstein theories of gravity. The emphasis is on qualitative features of the higher-spin gauge theory and peculiarities of its space-time interpretation. In particular, it is explained that Riemannian geometry cannot play a fundamental role in the higher-spin gauge theory. The higher-spin symmetries are argued to occur at ultra high energy scales beyond the Planck scale. This suggests that the higher-spin gauge theory can help to understand Quantum Gravity. Various types of higher-spin dualities are briefly discussed.Comment: 37 pages, no figures; V2: references adde

Geometric Second Order Field Equations for General Tensor Gauge Fields

Higher spin tensor gauge fields have natural gauge-invariant field equations written in terms of generalised curvatures, but these are typically of higher than second order in derivatives. We construct geometric second order field equations and actions for general higher spin boson fields, and first order ones for fermions, which are non-local but which become local on gauge-fixing, or on introducing auxiliary fields. This generalises the results of Francia and Sagnotti to all representations of the Lorentz group.Comment: 34 pages, LaTeX. Reference adde

Deformed Oscillator Algebras and Higher-Spin Gauge Interactions of Matter Fields in 2+1 Dimensions

We formulate a non-linear system of equations which describe higher-spin gauge interactions of massive matter fields in 2+1 dimensional space-time and explain some properties of the deformed oscillator algebra which underlies this formulation. In particular we show that the parameter of mass $M$ of matter fields is related to the deformation parameter in this algebra.Comment: LaTex, 12 pages, no figures; Invited talk at the International Seminar Supersymmetry and Quantum Field Theory dedicated to the memory of Dmitrij V. Volkov; Kharkov, January 1997; to appear in the proceeding

Holography of the N=1 Higher-Spin Theory on AdS4

We argue that the N=1 higher-spin theory on AdS4 is holographically dual to the N=1 supersymmetric critical O(N) vector model in three dimensions. This appears to be a special form of the AdS/CFT correspondence in which both regular and irregular bulk modes have similar roles and their interplay leads simultaneously to both the free and the interacting phases of the boundary theory. We study various boundary conditions that correspond to boundary deformations connecting, for large-N, the free and interacting boundary theories. We point out the importance of parity in this holography and elucidate the Higgs mechanism responsible for the breaking of higher-spin symmetry for subleading N.Comment: 19 page

Thermal compression of atomic hydrogen on helium surface

We describe experiments with spin-polarized atomic hydrogen gas adsorbed on liquid $^{4}$He surface. The surface gas density is increased locally by thermal compression up to $5.5\times10^{12}$ cm$^{-2}$ at 110 mK. This corresponds to the onset of quantum degeneracy with the thermal de-Broglie wavelength being 1.5 times larger than the mean interatomic spacing. The atoms were detected directly with a 129 GHz electron-spin resonance spectrometer probing both the surface and the bulk gas. This, and the simultaneous measurement of the recombination power, allowed us to make accurate studies of the adsorption isotherm and the heat removal from the adsorbed hydrogen gas. From the data, we estimate the thermal contact between 2D hydrogen gas and phonons of the helium film. We analyze the limitations of the thermal compression method and the possibility to reach the superfluid transition in 2D hydrogen gas.Comment: 20 pages, 11 figure

Evaluating the AdS dual of the critical O(N) vector model

We argue that the AdS dual of the three dimensional critical O(N) vector model can be evaluated using the Legendre transform that relates the generating functionals of the free UV and the interacting IR fixed points of the boundary theory. As an example, we use our proposal to evaluate the minimal bulk action of the scalar field that it is dual to the spin-zero ``current'' of the O(N) vector model. We find that the cubic bulk self interaction coupling vanishes. We briefly discuss the implications of our results for higher spin theories and comment on the bulk-boundary duality for subleading N.Comment: 17 pages, 1 figure, v2 references added, JHEP versio

Conformal Higher Spin Symmetries of 4d Massless Supermultiplets and osp(L,2M)osp(L,2M) Invariant Equations in Generalized (Super)Space

Realization of the conformal higher spin symmetry on the 4d massless field supermultiplets is given. The self-conjugated supermultiplets, including the linearized ${\cal N}=4$ SYM theory, are considered in some detail. Duality between non-unitary field-theoretical representations and the unitary doubleton--type representations of the 4d conformal algebra $su(2,2)$ is formulated in terms of a Bogolyubov transform. The set of 4d massless fields of all spins is shown to form a representation of $sp(8)$. The obtained results are extended to the generalized superspace invariant under $osp(L, 2M)$ supersymmetries. World line particle interpretation of the free higher spin theories in the $osp(2\N, 2M)$ invariant (super)space is given. Compatible with unitarity free equations of motion in the $osp(L,2M)$ invariant (super)space are formulated. A conjecture on the chain of $AdS_{d+1}/CFT_d \to AdS_{d}/CFT_{d-1} \to ...$ dualities in the higher spin gauge theories is proposed.Comment: Latex, 63 pages; no figures.V2 Typos corrected, References updated. V3.Typos correced, references and an explanation on the relationship with previous work in section 4 are added. The version to appear in Phys.Rev.

Higher Spins from Tensorial Charges and OSp(N|2n) Symmetry

It is shown that the quantization of a superparticle propagating in an N=1, D=4 superspace extended with tensorial coordinates results in an infinite tower of massless spin states satisfying the Vasiliev unfolded equations for free higher spin fields in flat and AdS_4 N=1 superspace. The tensorial extension of the AdS_4 superspace is proved to be a supergroup manifold OSp(1|4). The model is manifestly invariant under an OSp(N|8) (N=1,2) superconformal symmetry. As a byproduct, we find that the Cartan forms of arbitrary Sp(2n) and OSp(1|2n) groups are GL(2n) flat, i.e. they are equivalent to flat Cartan forms up to a GL(2n) rotation. This property is crucial for carrying out the quantization of the particle model on OSp(1|4) and getting the higher spin field dynamics in super AdS_4, which can be performed in a way analogous to the flat case.Comment: LaTeX, 21 page (JHEP style), misprints corrected, added comments on the relation of results of hep-th/0106149 with hep-th/9904109 and hep-th/9907113, references adde

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

On the covariant quantization of tensionless bosonic strings in AdS spacetime

The covariant quantization of the tensionless free bosonic (open and closed) strings in AdS spaces is obtained. This is done by representing the AdS space as an hyperboloid in a flat auxiliary space and by studying the resulting string constrained hamiltonian system in the tensionless limit. It turns out that the constraint algebra simplifies in the tensionless case in such a way that the closed BRST quantization can be formulated and the theory admits then an explicit covariant quantization scheme. This holds for any value of the dimension of the AdS space.Comment: 1+16 pages; v4 two clarifications adde