Theory for multiple partially massless spin-2 fields

Abstract

We revisit the problem of building consistent interactions for a multiplet of partially massless spin-2 fields in (anti-)de Sitter space. After rederiving and strengthening the existing no-go result on the impossibility of Yang-Mills type non-abelian deformations of the partially massless gauge algebra, we prove the uniqueness of the cubic interaction vertex and field-dependent gauge transformation that generalize the structures known from single-field analyses. Unlike in the case of one partially massless field, however, we show that for two or more particle species the cubic deformations can be made consistent at the complete non-linear level, albeit at the expense of allowing for negative relative signs between kinetic terms, making our new theory akin to conformal gravity. Our construction thus provides the first example of an interacting theory containing only partially massless fields.

The cosmological bootstrap: weight-shifting operators and scalar seeds

“…These shapes uniquely characterize the presence of PM fields of various depths in the early universe. Whether consistent interacting theories of those PM fields (beyond gravity and gauge theory) exist remains an open problem (but see [84,85]).…”

Pure Lorentz spin connection theories and uniqueness of general relativity

“…Poincaré gauge theory also exhibits this phenomenon quite generically [17]. Another popular example are partially massless graviton theories, where the linear theory on (A)dS propagates only the {±1, ±2} helicities of a massive graviton thanks to an Abelian U(1) gauge symmetry [20,21], but this symmetry cannot survive non-linearly [22,23] unless the theory includes ghosts [24,25]. In that case the prime example is conformal gravity, where the spectrum around (A)dS is a massless graviton and a partially-massless ghost graviton [26][27][28] and the aforementioned U(1) symmetry is the combination of a conformal transformation and a diffeomorphism.…”

Interactions for Partially-Massless Spin-2 Fields

“…Similarly to their Fronsdal cousins [15], interactions of higher spin PM fields are highly constrained by their gauge structure, and in fact no fully satisfactory examples of interacting higher-spin theories with PM fields are known (see however [16,17] for an intriguing proposal of a Vasiliev-like PM theory, and [18] for a proposal in three dimensions). While a few interesting studies have tackled the problem in the case of PM particles with spin s > 2 [19][20][21], the most detailed analyses have been focused on PM fields of spin s = 2 [22][23][24][25][26][27][28][29]. One reason is that this is of course the most technically tractable case, but there is also the more physical motivation that PM spin-2 fields may have some connection with theories of massive gravity [30][31][32][33][34][35].…”

“…One reason is that this is of course the most technically tractable case, but there is also the more physical motivation that PM spin-2 fields may have some connection with theories of massive gravity [30][31][32][33][34][35]. Cubic couplings involving PM gravitons have in particular been subject of several studies [29,[36][37][38]. It is by now well established that three-point vertices for PM spin-2 particles are forbidden, at least if one assumes up to two-derivative interactions and the absence of "ghost-like" fields, i.e.…”