The de Sitter group and its presence at the late-time boundary

Şengör, Gizem

doi:10.22323/1.406.0356

Cited by 7 publications

(9 citation statements)

References 8 publications

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“…The non-unitarity of the strictly and partially massless spin-s = 3/2, 5/2 fields on dS N for N ̸ = 4 was missed in [3], apparently because the dS invariant norm of the corresponding eigenmodes was not examined. For recent discussions on integer-spin representations of the dS group see [17,[18][19][20][21][22][23], while spin-1/2 representations have been discussed in [24,25]. A 'field theory-representation theory' dictionary for unitary totally symmetric tensor-spinors of any half-odd-integer spin s ⩾ 1/2 on dS N has been proposed in our previous article [1].…”

Section: Technical Explanation Of the Main Resultsmentioning

confidence: 99%

“…Similarly, as equations (5. 19) and (5.20) indicate, there is no type-I mode with θ N θ N -component given by equation (5.10) with ℓ = 1. Also, as demonstrated in appendix D, the quantisation condition (5.4) for the eigenvalue, as well as the condition n − ℓ ⩾ 0, arise as the requirement for the absence of singularity in the functions ϕ (5.21)…”

Section: Allowed Values For Angular Momentum Quantum Numbersmentioning

confidence: 98%

“…By integrating equation (8.23) over S N−1 we find that the scalar product (8. 19) is dS invariant, as…”

Section: Strictly/partially Massless Spin-3/2 and Spin-5/2 Representa...mentioning

confidence: 99%

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(Non-)unitarity of strictly and partially massless fermions on de Sitter space II: an explanation based on the group-theoretic properties of the spin-3/2 and spin-5/2 eigenmodes

Letsios

2024

J. Phys. A: Math. Theor.

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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.

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Section: Technical Explanation Of the Main Resultsmentioning

confidence: 99%

Section: Allowed Values For Angular Momentum Quantum Numbersmentioning

confidence: 98%

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(Non-)unitarity of strictly and partially massless fermions on de Sitter space II: an explanation based on the group-theoretic properties of the spin-3/2 and spin-5/2 eigenmodes

Letsios

2024

J. Phys. A: Math. Theor.

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“…In the basis of maximally compact subgroup generator L 0 , using our normalized late-time operators we can build states, as we did in (17), which we also know are labeled by the Casimir eigenvalue ∆ and the maximally compact subgroup eigenvalue n…”

Section: Massless Scalar Highest and Lowest Weight Statesmentioning

confidence: 99%

“…Here we will only review the discrete series inner product and hence the discrete series intertwining operator to the extend we need to make use of. A short review on the properties of the discrete series representation can also be found in [17].…”

Section: Summary Of Subgroups Of So(d + 1 1) and Unitaritymentioning

confidence: 99%

Principal and Complementary Series Representations at the Late-Time Boundary of de Sitter

Şengör

Skordis

2022

Springer Proceedings in Mathematics &Amp; Statistics

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The group SO(d + 1, 1) makes an appearance both as the conformal group of Euclidean space in d dimensions and as the isometry group of de Sitter spacetime in d + 1 dimensions. While this common feature can be taken as a hint towards holography on de Sitter space, understanding the representation theory has importance for cosmological applications where de Sitter spacetime is relevant. Among the categories of SO(d + 1, 1) unitary irreducible representations, discrete series is important in physical applications because they are expected to capture gauge fields. However, they are also the most difficult ones to recognize in field theoretical examples compared to representations from the other categories. Here we point towards some examples where we are able to recognize discrete series representations from fields on de Sitter and highlight some of the properties of these representations.

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

Şengör,

Skordis

2024

J. High Energ. Phys.

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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.

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The de Sitter group and its presence at the late-time boundary

Cited by 7 publications

References 8 publications

(Non-)unitarity of strictly and partially massless fermions on de Sitter space II: an explanation based on the group-theoretic properties of the spin-3/2 and spin-5/2 eigenmodes

(Non-)unitarity of strictly and partially massless fermions on de Sitter space II: an explanation based on the group-theoretic properties of the spin-3/2 and spin-5/2 eigenmodes

Principal and Complementary Series Representations at the Late-Time Boundary of de Sitter

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

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