On conformal higher spin wave operators

We analyze free conformal higher spin actions and the corresponding wave operators in arbitrary even dimensions and backgrounds. We show that the wave operators do not factorize in general, and identify the Weyl tensor and its derivatives as the obstruction to factorization. We give a manifestly factorized form for them on (A)dS backgrounds for arbitrary spin and on Einstein backgrounds for spin 2. We are also able to fix the conformal wave operator in d=4 for s=3 up to linear order in the Riemann tensor on generic Bach-flat backgrounds.Comment: 26 pages, includes Mathematica notebook. Version published in JHE

Feynman rules for higher-spin gauge fields on AdSd+1_{d+1}

We determine the Feynman rules for the minimal type A higher-spin gauge theory on AdS$_{d+1}$ at cubic order. In particular, we establish the quantum action at cubic order in de Donder gauge, including ghosts. We also give the full de Donder gauge propagators of higher-spin gauge fields and their ghosts. This provides all ingredients needed to quantise the theory at cubic order.Comment: v2: 32 pages, typos fixed, refs adde

Spinning Witten Diagrams

We develop a systematic framework to compute the conformal partial wave expansions (CPWEs) of tree-level four-point Witten diagrams with totally symmetric external fields of arbitrary mass and integer spin in AdS$_{d+1}$. Employing this framework, we determine the CPWE of a generic exchange Witten diagram with spinning exchanged field. As an intermediate step, we diagonalise the linear map between spinning three-point conformal structures and spinning cubic couplings in AdS. As a concrete application, we compute all exchange diagrams in the type A higher-spin gauge theory on AdS$_{d+1}$, which is conjectured to be dual to the free scalar $O\left(N\right)$ model. Given a CFT$_d$, our results provide the complete holographic reconstruction of all cubic couplings involving totally symmetric fields in the putative dual theory on AdS$_{d+1}$.Comment: 41 pages, many figures. v2: Three self-contained pages removed from section 4, to be restored elsewhere. Main results unaffected. Refs added and typos fixe

From Higher Spins to Strings: A Primer

A contribution to the collection of reviews "Introduction to Higher Spin Theory" edited by S. Fredenhagen, this introductory article is a pedagogical account of higher-spin fields and their connections with String Theory. We start with the motivations for and a brief historical overview of the subject. We discuss the Wigner classifications of unitary irreducible Poincar\'e-modules, write down covariant field equations for totally symmetric massive and massless representations in flat space, and consider their Lagrangian formulation. After an elementary exposition of the AdS unitary representations, we review the key no-go and yes-go results concerning higher-spin interactions, e.g., the Velo-Zwanziger acausality and its string-theoretic resolution among others. The unfolded formalism, which underlies Vasiliev's equations, is then introduced to reformulate the flat-space Bargmann-Wigner equations and the AdS massive-scalar Klein-Gordon equation, and to state the "central on-mass-shell theorem". These techniques are used for deriving the unfolded form of the boundary-to-bulk propagator in $AdS_4$, which in turn discloses the asymptotic symmetries of (supersymmetric) higher-spin theories. The implications for string-higher-spin dualities revealed by this analysis are then elaborated.Comment: 106 pages, 2 figures. Contribution to the collection of reviews "Introduction to Higher Spin Theory" edited by S. Fredenhagen. V2: Typos corrected, acknowledgements and references adde

Higher-Spin Gauge Theories and Bulk Locality

We present a no-go result on consistent Noether interactions among higher-spin gauge fields on anti-de Sitter space-times. We show that there is a non-local obstruction at the classical level to consistent interacting field theory descriptions of massless higher-spin particles that are described in the free limit by the free Fronsdal action, under the assumption that such theories arise from the gauging of a global higher-spin symmetry. Our result suggests that the Fronsdal programme for introducing interactions among higher-spin gauge fields cannot be completed without introducing new guiding principles, which could lie beyond the framework of classical field theory.Comment: 10 pages + refs. v2: Improved presentation, clarifications and references added. Some parts removed which just reviewed previous published work. To appear in Physical Review Letter

On Locality, Holography and Unfolding

We study the functional class and locality problems in the context of higher-spin theories and Vasiliev's equations. A locality criterion that is sufficient to make higher-spin theories well-defined as field theories on Anti-de-Sitter space is proposed. This criterion identifies admissible pseudo-local field redefinitions which preserve AdS/CFT correlation functions as we check in the 3d example. Implications of this analysis for known higher-spin theories are discussed. We also check that the cubic coupling coefficients previously fixed in 3d at the action level give the correct CFT correlation functions upon computing the corresponding Witten diagrams.Comment: 36 pages, LaTex. References added, typos corrected. Final version to appear in JHE

Higher Spins and String Interactions

In this Thesis we address the issue of consistent higher-spin interactions taking String Theory as a "theoretical laboratory". We thus arrive at a simple expression encompassing all three-point amplitudes for states belonging to the first Regge trajectory of the open bosonic string, that are described by fully symmetric tensors, and we explicitly construct the corresponding effective action at the cubic level. A gauge invariant structure is seen to emerge in the massless limit, in line with long-held expectations for high-energy string scattering. We also study some properties of the field theory amplitudes that arise from our effective Lagrangian and involve the exchange of infinitely many higher-spin excitations. These results and other related developments will soon appear in a joint publication with A. SagnottiComment: 95 pages, Master Thesis (Advisor: Prof. Augusto Sagnotti). v2:graduation date added, reference list fixed, references added. v3:typo corrected, reference adde

A Calculus for Higher Spin Interactions

Higher spin theories can be efficiently described in terms of auxiliary St\"uckelberg or projective space field multiplets. By considering how higher spin models couple to scale, these approaches can be unified in a conformal geometry/tractor calculus framework. We review these methods and apply them to higher spin vertices to obtain a generating function for massless, massive and partially massless three-point interactions.Comment: 24 pages, 3 figures, LaTex. References added, typos corrected. Final version to appear in JHE

Generating functions of (partially-)massless higher-spin cubic interactions

Generating functions encoding cubic interactions of (partially-)massless higher-spin fields are provided within the ambient-space formalism. They satisfy a system of higher-order partial differential equations that can be explicitly solved due to their factorized form. We find that the number of consistent couplings increases whenever the squares of the field masses take some integer values (in units of the cosmological constant) and satisfy certain conditions. Moreover, it is shown that only the supplemental solutions can give rise to non-Abelian deformations of the gauge symmetries. The presence of these conditions on the masses is a distinctive feature of (A)dS interactions that has in general no direct counterpart in flat space.Comment: 29 pages, 2 figures. References adde