Partial masslessness of higher spins in (A)dS

By S. Deser, A. Waldron. 2001

366 citations recorded by the source corpus.

Massive spin s ⩾ 3/2 fields can become partially massless in cosmological backgrounds. In the plane spanned by m^2 and Λ, there are lines where new gauge invariances permit intermediate sets of higher helicities, rather than the usual flat space extremes of all 2s + 1 massive or just 2 massless helicities. These gauge lines divide the (m2,Λ) plane into unitarily allowed or forbidden intermediate regions where all 2s + 1 massive helicities propagate but lower helicity states can have negative norms. We derive these consequences for s = 3/2,2 by studying both their canonical (anti)commutators and the transmutation of massive constraints to partially massless Bianchi identities. For s = 2, a Hamiltonian analysis exhibits the absence of zero helicity modes in the partially massless sector. For s =5/2,3 we derive Bianchi identities and their accompanying gauge invariances for the various partially massless theories with propagating helicities (±5/2,±3/2) and (±3,±2), (±3,±2,±1), respectively. Of these, only the s = 3 models are unitary. To these ends, we also provide the half integer generalization of the integer spin wave operators of Lichnerowicz. Partial masslessness applies to all higher spins in (A)dS as seen by their degree of freedom counts. Finally a derivation of massive d = 4 constraints by dimensional reduction from their d = 5 massless Bianchi identity ancestors is given.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d9ce512e31d50642a196916e4931354649c17942

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Citations in the corpus

Gauge gravity duality for d-wave superconductors: prospects and challenges (2010, background): “In [26, 30, 31] (see also [32]) it was shown that also from the bulk point of view, stability implies that m(2) ≥ 0.”
The Cosmological Bootstrap: Spinning correlators from symmetries and factorization (2020, background): “The representation with t = ` − 1 is a massless field, other values of t correspond to partially massless fields [133–135].”
Heavy spin-2 Dark Matter (2016, background): “At the point of saturation a linear gauge symmetry makes the helicity-0 mode of the massive spin-2 field non-dynamical [52, 53].”
Cosmological stability bound in massive gravity and bigravity (2013, background): “An intriguing, special, case of the Higuchi bound is what characterizes the so-called partially massless (PM) theory of massive gravity [62–75].”
Bootstrapping inflationary correlators in Mellin space (2019, background): “The divergences of the coefficients c (`) m are associated with the emergence of gauge symmetries in the bulk, where some of the helicity components decouple (see also [29, 89–93]).”
The cosmological bootstrap: weight-shifting operators and scalar seeds (2019, background): “These PM fields are unitary spinning representations that exist on (anti) de Sitter space, but have no flat-space counterparts [49, 74–79].”
Stability of Massive Cosmological Gravitons (2001, background): “…-t h/ 01 03 25 5v 2 We analyze the physics of massive spin 2 fields in (A)dS backgrounds and exhibit that: The theory is stable only for massesm2 ≥ 2Λ/3, where the conserved energy associated with the background timelike Klling vector is positive, while the instability form2 2Λ/3 is…”
Beyond the Cosmological Standard Model (2014, positive): “A further enticing possibility is that a particular choice of the potential terms could lead to an extra gauge symmetry about de Sitter space, leading to a theory of partially massless gravity [751, 752].”
Unfolding mixed-symmetry fields in AdS and the BMV conjecture: I. General formalism (2008, background): “Totally symmetric partially massless fields were first discussed in [47] and further studied in [48, 49] (see also [50] and references therein).”
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