The discreet charm of the discrete series in dS 2

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We calculate two-point functions of scalar fields of mass m and their conjugate momenta at the late-time boundary of de Sitter with Bunch-Davies boundary conditions, in general d + 1 spacetime dimensions. We perform the calculation using the wavefunction picture and using canonical quantization. With the latter one clearly sees how the late-time field and conjugate momentum operators are linear combinations of the normalized late-time operators αN and βN that correspond to unitary irreducible representations of the de Sitter group with well-defined inner products. The two-point functions resulting from these two different methods are equal and we find that both the autocorrelations of αN and βN and their cross correlations contribute to the late-time field and conjugate momentum two-point functions. This happens both for light scalars $$ \left(m<\frac{d}{2}H\right) $$ m < d 2 H , corresponding to complementary series representations, and heavy scalars $$ \left(m>\frac{d}{2}H\right) $$ m > d 2 H , corresponding to principal series representations of the de Sitter group, where H is the Hubble scale of de Sitter. In the special case m = 0, only the βN autocorrelation contributes to the conjugate momentum two-point function in any dimensions and we gather hints that suggest αN to correspond to discrete series representations for this case at d = 3.

Section: Two-point Functions For Light Scalarsmentioning

confidence: 99%

“…We will see such contact terms in sections 3.2.2 for discrete series operators and 3.2.3 in the case of principal series late-time operators. However more care must be given whether this statement on contact terms can be carried further to the late-time limit of discrete series field two-point functions [51].…”

Section: Two-point Functions For Light Scalarsmentioning

confidence: 99%

Scalar two-point functions at the late-time boundary of de Sitter

Şengör,

Skordis

2024

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New conformal-like symmetry of strictly massless fermions in four-dimensional de Sitter space

Letsios

2024

We present new infinitesimal ‘conformal-like’ symmetries for the field equations of strictly massless spin-s ≥ 3/2 totally symmetric tensor-spinors (i.e. gauge potentials) on 4-dimensional de Sitter spacetime (dS4). The corresponding symmetry transformations are generated by the five closed conformal Killing vectors of dS4, but they are not conventional conformal transformations. We show that the algebra generated by the ten de Sitter (dS) symmetries and the five conformal-like symmetries closes on the conformal-like algebra so(2, 4) up to gauge transformations of the gauge potentials. The transformations of the gauge-invariant field strength tensor-spinors under the conformal-like symmetries are given by the product of γ5 times a usual infinitesimal conformal transformation of the field strengths. Furthermore, we demonstrate that the two sets of physical mode solutions, corresponding to the two helicities ±s of the strictly massless theories, form a direct sum of Unitary Irreducible Representations (UIRs) of the conformal-like algebra. We also fill a gap in the literature by explaining how these physical modes form a direct sum of Discrete Series UIRs of the dS algebra so(1, 4).

Dualities among massive, partially massless and shift symmetric fields on (A)dS

Hinterbichler

2024

We catalog all the electromagnetic-like dualities that exist between free dynamical bosonic fields of arbitrary symmetry type and mass on (anti-) de Sitter space in all dimensions, including dualities among the partially massless and shift symmetric fields. This generalizes to all these field types the well known fact that a massless p-form is dual to a massless (D − p − 2)-form in D spacetime dimensions. In the process, we describe the structure of the Weyl modules (the spaces of local operators linear in the fields and their derivative relations) for all the massive, partially massless and shift symmetric fields.