Abstract
We use the formulation of conformal higher spin (CHS) theories in twistor space to study their tree-level scattering amplitudes, finding expressions for all three-point overline{mathrm{MHV}} amplitudes and all MHV amplitudes involving positive helicity conformal gravity particles and two negative helicity higher spins. This provides the on-shell analogue for the covariant coupling of CHS fields to a conformal gravity background. We discuss the restriction of the theory to a ghost-free unitary subsector, analogous to restricting conformal gravity to general relativity with a cosmological constant. We study the flat-space limit and show that the restricted amplitudes vanish, supporting the conjecture that in the unitary sector the S-matrix of CHS theories is trivial. However, by appropriately rescaling the amplitudes we find non-vanishing results which we compare with chiral flat-space higher spin theories.
Highlights
We use the formulation of conformal higher spin (CHS) theories in twistor space to study their tree-level scattering amplitudes, finding expressions for all three-point MHV amplitudes and all MHV amplitudes involving positive helicity conformal gravity particles and two negative helicity higher spins
We describe a unitary subsector of CHS theory, and discuss the various ways that external states of arbitrary spin are represented in twistor space
For the CHS theory we might hope to find analogous behaviour, which is to say that upon truncation to the unitary sector we find a massless higher spin theory on an AdS background where the dimensionful couplings are related to the dimensionless CHS
Summary
Conformal higher spin (CHS) theories were first formulated at the linearized level in terms of rank s symmetric fields φμ1···μs with free action [3]. The action (2.1) is invariant under both the local (differential) and algebraic (Weyl) gauge symmetries δφμ1···μs (x) = ∂(μ1 ǫμ2···μs)(x) − δ(μ1μ2 αμ3···μs)(x) for totally symmetric ǫμ(s−1)(x) and αμ(s−2)(x). These free theories were extended to cubic interactions some time ago [4, 16], and can be completed to an interacting CHS theory involving single copies of conformal fields at all spins for integer s ≥ 0 [5, 7, 8]. We review the formulation of CHS theory in twistor space [14], making use of a perturbative expansion around a self-dual (SD) sector. We describe a unitary subsector of CHS theory, and discuss the various ways that external states of arbitrary spin are represented in twistor space
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