Riassunto della Tesi di Laurea
Higher Spins and String Interactions
Field Theory has long experienced a conceptual barrier at spin two. In fact, the description of fundamental particles involves fields whose spin is at most one, insofar as the strong, weak and electromagnetic interactions are concerned, while macroscopic gravity interactions are related to a spin-two field, and in supersymmetric cases also to spin-3/2 fields.
In general, by higher-spin fields one means generalizations of the electromagnetic potential or of the metric fluctuation that transform under arbitrary representations of the Lorentz group. In four dimensions and up to dualities this set is exhausted by symmetric fields, while in higher dimensions one generally needs to consider generalizations of these tensors with mixed symmetry.
Conceptual difficulties have long been identified in attempts to couple massless higher-spin modes in a Minkowski background. However, the key classic no-go theorems rest, in one way or another, on the hypothesis that a finite number of such fields be present, and as a result their restrictions typically do not apply in the presence of infinite numbers of them. At any rate, it is important to explore directly these limitations and to see if and how they can be evaded.
Actually, two very distinct settings for higher-spin interactions are presently available. The first, provided by String Theory, embodies an infinite number of massive higher-spin modes in Minkowski backgrounds, while the second, provided by the Vasiliev construction, embodies an infinite number of massless higher-spin modes in (A)dS backgrounds. String Theory clearly leads the way to date, since its spectra involve a plethora of mixed-symmetry modes, while the Vasiliev construction involves only fully symmetric tensors, corresponding somehow to the first Regge trajectory of the open bosonic string. However, a key question is whether String Theory itself is part of a more general structure for higher-spin interactions, and what role it possibly plays in it.
For massive fields, one expects that an effective Lagrangian description be possible below the scale of their masses, and therefore in this Thesis I take String Theory as a starting point to exhibit for the first time a number of couplings involving higher-spin modes and corresponding Noether currents. From a string perspective, the novelty is here the explicit computation of tree-level scattering amplitudes for massive modes, to be contrasted with the massless excitations that are usually analyzed. On the field theory side, once the couplings are known one can convert them into Lagrangian interactions that can be conveniently deformed from Minkowski to (A)dS backgrounds. All this clearly opens the concrete possibility to delve more deeply into general features of higher-spin couplings. The Weyl calculus allows to present the whole set of cubic and quartic string couplings and the resulting currents in a compact and suggestive form.