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At the free level, a given massless field can be described by an infinite number of different potentials related to each other by dualities. In terms of Young tableaux, dualities replace any number of columns of height $h_i$ by columns of height $D-2-h_i$, where $D$ is the spacetime dimension: in particular, applying this operation to empty columns gives rise to potentials containing an arbitrary number of groups of $D-2$ extra antisymmetric indices. Using the method of parent actions, action principles including these potentials, but also extra fields, can be derived from the usual ones. In this paper, we revisit this off-shell duality and clarify the counting of degrees of freedom and the role of the extra fields. Among others, we consider the examples of the double dual graviton in $D=5$ and two cases, one topological and one dynamical, of exotic dualities leading to spin three fields in $D=3$.
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We obtain the higher spin tractor equations of motion conjectured by Gover et al. from a BRST approach and use those methods to prove that they describe massive, partially massless and massless higher spins in conformally flat backgrounds. The tractor description makes invariance under local choices of unit system manifest. In this approach, physical systems are described by conformal, rather than (pseudo-)Riemannian geometry. In particular masses become geometric quantities, namely the weights of tractor fields. Massive systems can therefore be handled in a unified and simple manner mimicking the gauge principle usually employed for massless models. From a holographic viewpoint, these models describe both the bulk and boundary theories in terms of conformal geometry. This is an important advance, because tying the boundary conformal structure to that of the bulk theory gives greater control over a bulk--boundary correspondence.
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 Poincare-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 Vasilievs 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.
The main purpose of this work is to show that massless Dirac equation formulated for non-interacting Majorana-Weyl spinors in higher dimensions, particularly in D=1+9 and D=5+5, can lead to an interpretation of massive Majorana and Dirac spinors in D=1+3. By adopting suitable representations of the Dirac matrices in higher dimensions, we pursue the investigation of which higher dimensional space-times and which mass-shell relation concerning massless Dirac equations in higher dimensions may induce massive spinors in D=1+3. The mixing of the chiral fermions in higher dimensions may induce a mechanism such that four massive Majorana fermions may show up and, at an appropriate limit an almost zero and a huge mass show up with corresponding left-handed and right-handed eigenstates. This mechanism, in a peculiar way, could reassess the See-Saw scheme associated to neutrino with Majorana-type masses. Remarkably the masses of the particles are fixed by the dimension decoupling/reduction scheme based on the mass Lorentz invariant term, where one set of the decoupled dimensions are the target coordinates frame and the other set of coordinates is the composing block of the mass term in lower dimensions. This proposal should allow us to understand the generation of hierarchies, such as the fourth generation, for the fermionic masses in D=1+3, or in lower dimensions in general, starting from the constraints between the energy and the momentum in D=n+n. For the initial D=5+5 Majorana-Weyl spinors framework using the Weyl representation to the Dirac matrices we observe an intriguing decomposition of space-time that result in two very equivalent D=1+4 massive spinors which mass term, in D=1+3 included, is originated from the remained/decoupled component and that could induce a Brane-World mechanism.
The simplest higher-spin interactions involve classical external currents and symmetric tensors $phi_{m_1 ... m_s}$, and convey three instructive lessons. The first is a general form of the van Dam-Veltman-Zakharov discontinuity in flat space for this class of fields. The second is the rationale for its disappearance in (A)dS spaces. Finally, the third is a glimpse into an option which is commonly overlooked in Field Theory, and which both higher spins and String Theory are confronting us with: one can well allow in the Lagrangians non-local terms that do not spoil the local nature of physical quantities.
We study the implications on inflation of an infinite tower of higher-spin states with masses falling exponentially at large field distances, as dictated by the Swampland Distance Conjecture. We show that the Higuchi lower bound on the mass of the tower automatically translates into an upper bound on the inflaton excursion. Strikingly, the mere existence of all spins in the tower forbids any scalar displacement whatsoever, at arbitrarily small Hubble scales, and it turns out therefore incompatible with inflation. A certain field excursion is allowed only if the tower has a cut-off in spin. Finally, we show that this issue is circumvented in the case of a tower of string excitations precisely because of the existence of such a cut-off, which decreases fast enough in field space.
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