Abstract:The de Sitter spacetime is a maximally symmetric spacetime. It is one of the vacuum solutions to Einstein equations with a cosmological constant. It is the solution with a positive cosmological constant and describes a universe undergoing accelerated expansion. Among the possible signs for a cosmological constant, this solution is relevant for primordial and late-time cosmology. In the case of a zero cosmological constant, studies on the representations of its isometry group have led to a broader understanding… Show more
In this note we discuss features of the simplest spinning Discrete Series Unitary Irreducible Representations (UIR) of SO(1,4). These representations are known to be realised in the single particle Hilbert space of a free gauge field propagating in a four dimensional fixed de Sitter background. They showcase distinct features as compared to the more common Principal Series realised by heavy fields. Upon computing the 1 loop Sphere path integral we show that the edge modes of the theory can be understood in terms of a Discrete Series of SO(1, 2). We then canonically quantise the theory and show how group theory constrains the mode decomposition. We further clarify the role played by the second SO(4) Casimir in the single particle Hilbert space of the theory.
In this note we discuss features of the simplest spinning Discrete Series Unitary Irreducible Representations (UIR) of SO(1,4). These representations are known to be realised in the single particle Hilbert space of a free gauge field propagating in a four dimensional fixed de Sitter background. They showcase distinct features as compared to the more common Principal Series realised by heavy fields. Upon computing the 1 loop Sphere path integral we show that the edge modes of the theory can be understood in terms of a Discrete Series of SO(1, 2). We then canonically quantise the theory and show how group theory constrains the mode decomposition. We further clarify the role played by the second SO(4) Casimir in the single particle Hilbert space of the theory.
In our previous article [J. High Energ. Phys. 2023, 15 (2023)], we showed that the strictly massless spin-3/2 field, as well as the strictly and partially massless spin-5/2 fields, on N-dimensional (N ≧ 3) de Sitter spacetime (dSN) are non-unitary unless N=4. The (non-)unitarity was demonstrated by simply observing that there is a (mis-)match between the representation-theoretic labels that correspond to the Unitary Irreducible Representations (UIR's) of the de Sitter (dS) algebra spin(N,1) and the ones corresponding to the space of eigenmodes of the field theories. In this paper, we provide a technical representation-theoretic explanation for this fact by studying the (non-)existence of positive-definite, dS invariant scalar products for the spin-3/2 and spin-5/2 strictly/ partially massless eigenmodes on dSN (N ≧ 3). Our basic tool is the examination of the action of spin(N,1) generators on the space of eigenmodes, leading to the following findings. For odd N, any dS invariant scalar product is identically zero. For even N > 4, any dS invariant scalar product must be indefinite. This gives rise to positive-norm and negative-norm eigenmodes that mix with each other under spin(N,1) boosts. In the N=4 case, the positive-norm sector decouples from the negative-norm sector and each sector separately forms a UIR of spin(4,1). Our analysis makes extensive use of the analytic continuation of tensor-spinor spherical harmonics on the N-sphere (SN) to dSN and also introduces representation-theoretic techniques that are absent from the mathematical physics literature on half-odd-integer-spin fields on dSN.
In the context of weak-field metric-affine (i.e. Palatini) gravity near Minkowski spacetime, we compute the particle spectra in the simultaneous presence of all independent contractions quadratic in Ricci-type tensors. Apart from the full metric-affine geometry, we study kinematic limits with vanishing torsion (i.e. a symmetric connection) and vanishing nonmetricity (i.e. a metric connection, which is physically indistinguishable from Poincaré gauge theory at the level of the particle spectrum). We present a detailed report on how spin-parity projection operators can be used to derive systematically and unambiguously the character of the propagating states. The unitarity constraints derived from the requirements of tachyon and ghost freedom are obtained. We show that, even in the presence of all Ricci-type operators, only a narrow selection of viable theories emerges by a tuning.
Published by the American Physical Society
2024
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