Interactions of a massless tensor field with the mixed symmetry of the Riemann tensor. No-go results

Non-trivial, consistent interactions of a free, massless tensor field t_{\mu \nu |\alpha \beta} with the mixed symmetry of the Riemann tensor are studied in the following cases: self-couplings, cross-interactions with a Pauli-Fierz field and cross-couplings with purely matter theories. The main results, obtained from BRST cohomological techniques under the assumptions on smoothness, locality, Lorentz covariance and Poincar\'{e} invariance of the deformations, combined with the requirement that the interacting Lagrangian is at most second-order derivative, can be synthesized into: no consistent self-couplings exist, but a cosmological-like term; no cross-interactions with the Pauli-Fierz field can be added; no non-trivial consistent cross-couplings with the matter theories such that the matter fields gain gauge transformations are allowed.Comment: for version 3: 45 pages, uses amssymb; shortened version, the three appendices from version 2 can be found in hep-th/040209

Geometry and dynamics of higher-spin frame fields

We give a systematic account of unconstrained free bosonic higher-spin fields on D-dimensional Minkowski and (Anti-)de Sitter spaces in the frame formalism. The generalized spin connections are determined by solving a chain of torsion-like constraints. Via a generalization of the vielbein postulate these allow to determine higher-spin Christoffel symbols, whose relation to the de Wit--Freedman connections is discussed. We prove that the generalized Einstein equations, despite being of higher-derivative order, give rise to the AdS Fronsdal equations in the compensator formulation. To this end we derive Damour-Deser identities for arbitrary spin on AdS. Finally we discuss the possibility of a geometrical and local action principle, which is manifestly invariant under unconstrained higher-spin symmetries.Comment: 30 pages, uses youngtab.sty, v2: minor changes, references adde

Interactions between a massless tensor field with the mixed symmetry of the Riemann tensor and a massless vector field

Consistent couplings between a massless tensor field with the mixed symmetry of the Riemann tensor and a massless vector field are analyzed in the framework of Lagrangian BRST cohomology. Under the assumptions on smoothness, locality, Lorentz covariance, and Poincare invariance of the deformations, combined with the requirement that the interacting Lagrangian is at most second-order derivative, it is proved that there are no consistent cross-interactions between a single massless tensor field with the mixed symmetry of the Riemann tensor and one massless vector field.Comment: LaTeX, 24 page

Consistent interactions of dual linearized gravity in D=5: couplings with a topological BF model

Under some plausible assumptions, we find that the dual formulation of linearized gravity in D=5 can be nontrivially coupled to the topological BF model in such a way that the interacting theory exhibits a deformed gauge algebra and some deformed, on-shell reducibility relations. Moreover, the tensor field with the mixed symmetry (2,1) gains some shift gauge transformations with parameters from the BF sector.Comment: 63 pages, accepted for publication in Eur. Phys. J.

Classification of non-Riemannian doubled-yet-gauged spacetime

Assuming $\mathbf{O}(D,D)$ covariant fields as the `fundamental' variables, Double Field Theory can accommodate novel geometries where a Riemannian metric cannot be defined, even locally. Here we present a complete classification of such non-Riemannian spacetimes in terms of two non-negative integers, $(n,\bar{n})$, $0\leq n+\bar{n}\leq D$. Upon these backgrounds, strings become chiral and anti-chiral over $n$ and $\bar{n}$ directions respectively, while particles and strings are frozen over the $n+\bar{n}$ directions. In particular, we identify $(0,0)$ as Riemannian manifolds, $(1,0)$ as non-relativistic spacetime, $(1,1)$ as Gomis-Ooguri non-relativistic string, $(D{-1},0)$ as ultra-relativistic Carroll geometry, and $(D,0)$ as Siegel's chiral string. Combined with a covariant Kaluza-Klein ansatz which we further spell, $(0,1)$ leads to Newton-Cartan gravity. Alternative to the conventional string compactifications on small manifolds, non-Riemannian spacetime such as $D=10$, $(3,3)$ may open a new scheme of the dimensional reduction from ten to four.Comment: 1+41 pages; v2) Refs added; v3) Published version; v4) Sign error in (2.51) correcte

Holography, Unfolding and Higher-Spin Theory

Holographic duality is argued to relate classes of models that have equivalent unfolded formulation, hence exhibiting different space-time visualizations for the same theory. This general phenomenon is illustrated by the $AdS_4$ higher-spin gauge theory shown to be dual to the theory of 3d conformal currents of all spins interacting with 3d conformal higher-spin fields of Chern-Simons type. Generally, the resulting 3d boundary conformal theory is nonlinear, providing an interacting version of the 3d boundary sigma model conjectured by Klebanov and Polyakov to be dual to the $AdS_4$ HS theory in the large $N$ limit. Being a gauge theory it escapes the conditions of the theorem of Maldacena and Zhiboedov, which force a 3d boundary conformal theory to be free. Two reductions of particular higher-spin gauge theories where boundary higher-spin gauge fields decouple from the currents and which have free boundary duals are identified. Higher-spin holographic duality is also discussed for the cases of $AdS_3/CFT_2$ and duality between higher-spin theories and nonrelativistic quantum mechanics. In the latter case it is shown in particular that ($dS$) $AdS$ geometry in the higher-spin setup is dual to the (inverted) harmonic potential in the quantum-mechanical setup.Comment: 57 pages, V2: Acknowledgements, references, comments, clarifications and new section on reductions of particular HS theories associated with free boundary theories are added. Typos corrected, V3. Minor corrections: clarification in section 9 is added and typos correcte

Higher Spin Scattering in Superstring Theory

We compute scattering amplitudes of leading Regge trajectory states in open superstring theories. Highest spin states at mass level n with spin s=n+1 for bosons and s=n+1/2 for fermions are generated by particularly simple vertex operators. Hence, the cubic couplings of bosons and fermions on the leading Regge trajectory are given for arbitrary n. The same can be achieved for higher point amplitudes, and this article focuses on four point level with one heavy maximum spin state and three massless states in any bose-fermi combination, putting particular emphasis on manifest cyclic symmetry. Except for the four fermion coupling, all our results remain valid in any D<10 dimensional compactification scenario, so they might become relevant at LHC in case of an experimentally accessible low string scale. But even if not directly observable, superstring amplitudes provide important clues on higher spin dynamics and their consistent interactions in field theory.Comment: 31 pages; v3: final version published in Nuclear Physics

On manifolds admitting the consistent Lagrangian formulation for higher spin fields

We study a possibility of Lagrangian formulation for free higher spin bosonic totally symmetric tensor field on the background manifold characterizing by the arbitrary metric, vector and third rank tensor fields in framework of BRST approach. Assuming existence of massless and flat limits in the Lagrangian and using the most general form of the operators of constraints we show that the algebra generated by these operators will be closed only for constant curvature space with no nontrivial coupling to the third rank tensor and the strength of the vector fields. This result finally proves that the consistent Lagrangian formulation at the conditions under consideration is possible only in constant curvature Riemann space.Comment: 11 pages; v2: minor typos corrected, a reference adde

No cross-interactions among different tensor fields with the mixed symmetry (3,1) intermediated by a vector field

Under the hypotheses of analyticity in the coupling constant, locality, Lorentz covariance, and Poincare invariance of the deformations, combined with the preservation of the number of derivatives on each field, the consistent interactions between a collection of free massless tensor gauge fields with the mixed symmetry of a two-column Young diagram of the type (3,1) and one Abelian vector field, respectively a $p$-form gauge field, are addressed. The main result is that a single mixed symmetry tensor field from the collection gets coupled to the vector field/$p$-form. Our final result resembles to the well known fact from General Relativity according to which there is one graviton in a given world.Comment: 19 page

Two-dimensional interactions between a BF-type theory and a collection of vector fields

Consistent interactions that can be added to a two-dimensional, free abelian gauge theory comprising a special class of BF-type models and a collection of vector fields are constructed from the deformation of the solution to the master equation based on specific cohomological techniques. The deformation procedure modifies the Lagrangian action, the gauge transformations, as well as the accompanying algebra of the interacting model.Comment: LaTeX 2e, 31 page