Scattering of conformal higher spin fields

We develop a formalism for describing the most general notion of tree-level scattering amplitudes in 4d conformal higher spin theory. As conformal higher spin fields obey higher-derivative equations of motion, there are many distinct on-shell external states which may contribute to their scattering, some of which grow polynomially with time, leading to ill-defined amplitudes. We characterize the set of admissible scattering states which produce finite tree amplitudes, noting that there are more such states than just standard massless higher spins obeying two-derivative equations of motion. We use conformal gravity as a prime example, where the set of scattering states includes the usual Einstein graviton and a `ghost' massless spin 1 particle. An extension of the usual spinor helicity formalism allows us to encode these scattering states efficiently in terms of `twistor-spinors'. This leads to compact momentum space expressions for all finite tree-level 3-point amplitudes of conformal higher spin theory. While some of these 3-point amplitudes vanish (including all those with only standard two-derivative higher spin external states), there are many others which are non-vanishing. We also comment on the generalization to scattering of conformal higher spins in AdS$_4$.Comment: 40 pages, no figures. v2: references adde

Conformal higher spins and scattering amplitudes

This thesis presents results pertaining to scattering amplitudes in Conformal Higher Spin (CHS) theory, most of which was published in \cite{Joung:2015eny, Beccaria:2016syk, Adamo:2018srx}. \\ CHS theory contains Maxwell theory, Conformal Gravity and generalises them for higher spin. After briefly introducing the general field of Higher Spins, we therefore discuss Conformal Gravity as a warm up. Since it is a 4-derivative theory, it contains more on-shell states than just the usual 2-derivative Einstein Gravitons. Some of these states are found to be admissible for scattering and lead to finite expressions for amplitudes. We compute three point tree-level amplitudes scattering all possible states. We give a formula which captures these amplitudes using twistor spinors. \\ We then define CHS theory and its symmetries. We descirbe how it is obtained as the logarithmically divergent part of the partition function for a free scalar coupled to general spin background sources. We characterise its scattering states and proceed to present a series of amplitude computations. \\ We first compute four-point amplitudes for an external scalar interacting with the full tower of CHS fields. These amplitudes need a natural prescription for summing over that infinite tower of fields. Doing so in a way that is compatible with CHS symmetry leads to vanishing amplitudes. \\ We then present similar amplitudes in pure CHS theory where the external legs are 2-derivative spin $1$ and 2 CHS modes. Once again, these amplitudes are trivial. As the theory is conformal, it has a natural description in the language of twistor-spinors and we give a formula for three-point tree level amplitudes of \emph{all} states, including those which are not associated with 2 derivative equations of motion. \\ Finally we look at the theory in curved spacetime, where its quadratic sector is non-diagonal. We compute some of these terms and their contributions to the conformal anomaly $c$-coefficient.Open Acces