A note on higher-derivative actions for free higher-spin fields

Abstract

Higher-derivative theories of free higher-spin fields are investigated focusing on their symmetries. Generalizing familiar two-derivative constrained formulations, we first construct less-constrained Einstein-like and Maxwell-like higher-derivative actions. Then, we construct Weyl-like actions-the actions admitting constrained Weyl symmetries-with different numbers of derivatives. They are presented in a factorized form making use of Einstein-like and Maxwell-like tensors. The last (highest-derivative) member of the hierarchy of the Weyl-like actions coincides with the Fradkin-Tseytlin conformal higherspin action in four dimensions.1 On leave from Yerevan Physics Institute.

On conformal higher spin wave operators

“…The main result of this paper is the explicit form of the wave operator on (A)dS backgrounds, together with the identification of the obstruction to factorization on more general backgrounds. The results of this paper confirm previous conjecture about conformal HS wave operators on (A)dS backgrounds [48,62]. On the other hand the identification of the obstruction to factorization for spin s > 2 HS wave operators on more general backgrounds lead us to reconsider modifications of this conjecture.…”

“…It is worth pointing out that the coefficients β precisely match the masses associated with the partially massless points for spin s, plus some discrete massive points in d > 4. This is in agreement with previous conjectures on conformal HS wave operators [48,62]. This implies in turn that the part of the conformal operator that is not proportional to divergences or traces has the form…”

“…Their combined mass spectrum comprises the massless and partiallymassless points plus massive points in higher dimensions [5,43,[55][56][57][58][59][60][61]. This provides additional evidence for previous conjectures made in [48,62] and extends them. In addition, we also identify the Weyl tensor and its derivatives as the obstruction to factorization for spin s > 2 on generic backgrounds.…”

“…3 See [48] for some discussion of higher derivative theories in flat space, [49,50] for some earlier discussion on conformal operators and [51][52][53][54] for selected math literature.…”

Multi-Hamiltonian formulations and stability of higher-derivative extensions of 3d Chern–Simons

“…Among most frequently studied specific models we can mention Pais-Uhlenbeck (PU) oscillator [1], Podolsky and LeeWick electrodynamics [2][3][4], higher-derivative extensions of the Chern-Simons model [5], higher-derivative Yang-Mills a e-mail: abakumova@phys.tsu.ru b e-mail: dsc@phys.tsu.ru c e-mail: sll@phys.tsu.ru models [6], conformal gravity [7], various higher-derivative higher-spin fields theories [8][9][10], modified theories of gravity [11], including critical gravity [12]. The higher-derivative models often reveal remarkable various properties comparing to the counterparts without higher derivatives.…”