Effective action in a higher-spin background

We consider a free massless scalar field coupled to an infinite tower of background higher-spin gauge fields via minimal coupling to the traceless conserved currents. The set of Abelian gauge transformations is deformed to the non-Abelian group of unitary operators acting on the scalar field. The gauge invariant effective action is computed perturbatively in the external fields. The structure of the various (divergent or finite) terms is determined. In particular, the quadratic part of the logarithmically divergent (or of the finite) term is expressed in terms of curvatures and related to conformal higher-spin gravity. The generalized higher-spin Weyl anomalies are also determined. The relation with the theory of interacting higher-spin gauge fields on anti de Sitter spacetime via the holographic correspondence is discussed.Comment: 40 pages, Some errors and typos corrected, Version published in JHE

A HIERARCHY OF GAUGED GRASSMANIAN MODELS IN 4p4p DIMENSIONS WITH SELF-DUAL INSTANTONS

We present a hierarchy of gauged Grassmanian models in $4p$ dimensions, where the gauge field takes its values in the $2^{2p- 1}\times 2^{2p-1}$ chiral representation of SO(4p). The actions of all these models are absolutely minimised by a hierarchy of self-duality equations, all of which reduce to a single pair of coupled ordinary differential equations when subjected to $4p$ dimensional spherical symmetry.Comment: latex file, 13 page

Spin 3 cubic vertices in a frame-like formalism

Till now most of the results on interaction vertices for massless higher spin fields were obtained in a metric-like formalism using completely symmetric (spin-)tensors. In this, the Lagrangians turn out to be very complicated and the main reason is that the higher the spin one want to consider the more derivatives one has to introduce. In this paper we show that such investigations can be greatly simplified if one works in a frame-like formalism. As an illustration we consider massless spin 3 particle and reconstruct a number of vertices describing its interactions with lower spin 2, 1 and 0 ones. In all cases considered we give explicit expressions for the Lagrangians and gauge transformations and check that the algebra of gauge transformations is indeed closed.Comment: 17 pades, no figure

Higher spin interactions with scalar matter on constant curvature spacetimes: conserved current and cubic coupling generating functions

Cubic couplings between a complex scalar field and a tower of symmetric tensor gauge fields of all ranks are investigated on any constant curvature spacetime of dimension d>2. Following Noether's method, the gauge fields interact with the scalar field via minimal coupling to the conserved currents. A symmetric conserved current, bilinear in the scalar field and containing up to r derivatives, is obtained for any rank r from its flat spacetime counterpart in dimension d+1, via a radial dimensional reduction valid precisely for the mass-square domain of unitarity in (anti) de Sitter spacetime of dimension d. The infinite collection of conserved currents and cubic vertices are summarized in a compact form by making use of generating functions and of the Weyl/Wigner quantization on constant curvature spaces.Comment: 35+1 pages, v2: two references added, typos corrected, enlarged discussions in Subsection 5.2 and in Conclusion, to appear in JHE

Higher-Spin Fermionic Gauge Fields and Their Electromagnetic Coupling

We study the electromagnetic coupling of massless higher-spin fermions in flat space. Under the assumptions of locality and Poincare invariance, we employ the BRST-BV cohomological methods to construct consistent parity-preserving off-shell cubic 1-s-s vertices. Consistency and non-triviality of the deformations not only rule out minimal coupling, but also restrict the possible number of derivatives. Our findings are in complete agreement with, but derived in a manner independent from, the light-cone-formulation results of Metsaev and the string-theory-inspired results of Sagnotti-Taronna. We prove that any gauge-algebra-preserving vertex cannot deform the gauge transformations. We also show that in a local theory, without additional dynamical higher-spin gauge fields, the non-abelian vertices are eliminated by the lack of consistent second-order deformations.Comment: 44 pages; references added, minor changes made, to appear in JHE

Maxwell-like Lagrangians for higher spins

We show how implementing invariance under divergence-free gauge transformations leads to a remarkably simple Lagrangian description of massless bosons of any spin. Our construction covers both flat and (A)dS backgrounds and extends to tensors of arbitrary mixed-symmetry type. Irreducible and traceless fields produce single-particle actions, while whenever trace constraints can be dispensed with the resulting Lagrangians display the same reducible, multi-particle spectra as those emerging from the tensionless limit of free open-string field theory. For all explored options the corresponding kinetic operators take essentially the same form as in the spin-one, Maxwell case.Comment: 77 pages, revised version. Erroneous interpretation and proof of the gauge-fixing procedure for mixed-symmetry fields corrected. As a consequence, the mixed-symmetry, one-particle Lagrangians are to be complemented with conditions on the divergences of the fields; all other conclusions unchanged. Additional minor changes including references added. To appear in JHE

Higher-Spin Interactions: four-point functions and beyond

In this work we construct an infinite class of four-point functions for massless higher-spin fields in flat space that are consistent with the gauge symmetry. In the Lagrangian picture, these reflect themselves in a peculiar non-local nature of the corresponding non-abelian higher-spin couplings implied by the Noether procedure that starts from the fourth order. We also comment on the nature of the colored spin-2 excitation present both in the open string spectrum and in the Vasiliev system, highlighting how some aspects of String Theory appear to reflect key properties of Field Theory that go beyond its low energy limit. A generalization of these results to n-point functions, fermions and mixed-symmetry fields is also addressed.Comment: 66 pages, 10 figures, 1 table, LaTex. Several statements clarified. Final version to appear in JHE

Asymptotic W-symmetries in three-dimensional higher-spin gauge theories

We discuss how to systematically compute the asymptotic symmetry algebras of generic three-dimensional bosonic higher-spin gauge theories in backgrounds that are asymptotically AdS. We apply these techniques to a one-parameter family of higher-spin gauge theories that can be considered as large N limits of SL(N) x SL(N) Chern-Simons theories, and we provide a closed formula for the structure constants of the resulting infinite-dimensional non-linear W-algebras. Along the way we provide a closed formula for the structure constants of all classical W_N algebras. In both examples the higher-spin generators of the W-algebras are Virasoro primaries. We eventually discuss how to relate our basis to a non-primary quadratic basis that was previously discussed in literature.Comment: 61 page

Half-integer Higher Spin Fields in (A)dS from Spinning Particle Models

We make use of O(2r+1) spinning particle models to construct linearized higher-spin curvatures in (A)dS spaces for fields of arbitrary half-integer spin propagating in a space of arbitrary (even) dimension: the field potentials, whose curvatures are computed with the present models, are spinor-tensors of mixed symmetry corresponding to Young tableaux with D/2 - 1 rows and r columns, thus reducing to totally symmetric spinor-tensors in four dimensions. The paper generalizes similar results obtained in the context of integer spins in (A)dS.Comment: 1+18 pages; minor changes in the notation, references updated. Published versio

A Note on Vectorial AdS5_5/CFT4_4 Duality for Spin-jj Boundary Theory

The vectorial holographic correspondences between higher-spin theories in AdS$_5$ and free vector models on the boundary are extended to the cases where the latter is described by free massless spin-$j$ field. The dual higher-spin theory in the bulk does not include gravity and can only be defined on rigid AdS$_5$ background with $S^4$ boundary. We discuss various properties of these rather special higher-spin theories and calculate their one-loop free energies. We show that the result is proportional to the same quantity for spin-$j$ doubleton treated as if it is a AdS$_5$ field. Finally, we consider even more special case where the boundary theory itself is given by an infinite tower of massless higher-spin fields.Comment: 27 pages, version to appear in JHE