34 research outputs found
Ordinary-derivative formulation of conformal totally symmetric arbitrary spin bosonic fields
Conformal totally symmetric arbitrary spin bosonic fields in flat space-time
of even dimension greater than or equal to four are studied. Second-derivative
(ordinary-derivative) formulation for such fields is developed. We obtain gauge
invariant Lagrangian and the corresponding gauge transformations. Gauge
symmetries are realized by involving the Stueckelberg and auxiliary fields.
Realization of global conformal boost symmetries on conformal gauge fields is
obtained. Modified de Donder gauge condition and de Donder-Stueckelberg gauge
condition are introduced. Using the de Donder-Stueckelberg gauge frame,
equivalence of the ordinary-derivative and higher-derivative approaches is
demonstrated. On-shell degrees of freedom of the arbitrary spin conformal field
are analyzed. Ordinary-derivative light-cone gauge Lagrangian of conformal
fields is also presented. Interrelations between the ordinary-derivative gauge
invariant formulation of conformal fields and the gauge invariant formulation
of massive fields are discussed.Comment: 51 pages, v2: Results and conclusions of v1 unchanged. In Sec.3,
brief review of higher-derivative approaches added. In Sec.4, new
representations for Lagrangian, modified de Donder gauge, and de
Donder-Stueckelberg gauge added. In Sec.5, discussion of interrelations
between the ordinary-derivative and higher-derivative approaches added.
Appendices A,B,C,D and references adde
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.Comment: 40 pages, no figures. v2: references adde