On triviality of S-matrix in conformal higher spin theory

Abstract

We consider the conformal higher spin (CHS) theory in d = 4 that contains the s = 1 Maxwell vector, s = 2 Weyl graviton and their higher spin s = 3, 4, . . . counterparts with higher-derivative s kinetic terms. The interacting action for such theory can be found as the coefficient of the logarithmically divergent part in the induced action for sources coupled to higher spin currents in a free complex scalar field model. We explicitly determine some cubic and quartic interaction vertices in the CHS action from scalar loop integrals. We then compute the simplest tree-level 4-particle scattering amplitudes 11→11, 22→22 and 11→22 and find that after summing up all the intermediate CHS exchanges they vanish. This generalises the vanishing of the scattering amplitude for external conformal scalars interacting via the exchange of all CHS fields found earlier in arXiv:1512.08896. This vanishing should generalise to all scattering amplitudes in the CHS theory and as in the conformal scalar scattering case should be a consequence of the underlying infinite dimensional higher spin symmetry that extends the standard conformal symmetry.

Investigations into light-front interactions for massless fields (I): non-constructibility of higher spin quartic amplitudes

“…In conformal higher spin theory [33] it was -for instance -found [34] that the four-scalar tree-level scattering amplitude with a tower of higher spins in the channel vanishes. See also [35] for further results. Similar results -amplitudes being delta-distributions rather than analytic functions -are also reported in the AdS/CFT context in [36] and [37].…”

“…See also comments in [39]. Somewhat ironically it may be the very existence of such a huge higher spin symmetry that constrains the scattering amplitudes to be trivial, as discussed in [35,36].…”

C T for conformal higher spin fields from partition function on conically deformed sphere

“…The log UV divergent contribution of the determinant of a single 2nd order Laplace-type operator can be computed as the value of the corresponding spectral zeta function at zero, i.e. 5 8) where d i are degeneracies of the eigenvalues λ i . The general structure of ζ(q) for a bosonic field will be as follows…”

“…8 The rest of this paper is organized as follows. In section 2 we shall find ζ(q) (1.8) for the Laplace-type spin s operators on S 4 q that enter the partition function of CHS fields.…”

“…Conformal higher spins in 4d [3][4][5][6][7][8] have higher derivative kinetic terms h s ∂ 2s h s (h s are totally symmetric rank s tensors) and thus their generalization to a curved metric background is a non-trivial question (cf. [1,2,9,10]).…”