Notes on gauge fields and discrete series representations in de Sitter spacetimes

Fukelman, Alan Rios; Sempé, Matías; Silva, Guillermo A.

doi:10.1007/jhep01(2024)011

Cited by 3 publications

(1 citation statement)

References 98 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Regarding gauge fields on de Sitter from a group theoretical perspective we highlight current literature. Unitarity allowed mass ranges for spin 1 and spin 2 fields on de Sitter were considered in [59]; in [60] a spin 1 field is classified in terms of which category of JHEP02(2024)076 de Sitter representations it falls under with respect to ranges of its mass; the recent work of [61] where the spin 1 gauge field with a U(1) symmetry is considered using canonical and path integral quantization for the purpose of exploring edge-modes from the perspective of representation theory. Fermions have recently been studied using a group theory approach in the work of [62] which discusses unitarity of spin 3/2 and the work of [63] which considers Wightman functions of fermions and tensors in de Sitter using embedding space formalism.…”

Section: Discussionmentioning

confidence: 99%

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

Şengör,

Skordis

2024

J. High Energ. Phys.

View full text Add to dashboard Cite

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.

show abstract

Section: Discussionmentioning

confidence: 99%

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

Şengör,

Skordis

2024

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

Unconventional conformal invariance of maximal depth partially massless fields on dS4 and its relation to complex partially massless SUSY

Letsios

2024

J. High Energ. Phys.

View full text Add to dashboard Cite

Deser and Waldron have shown that maximal depth partially massless theories of higher (integer) spin on four-dimensional de Sitter spacetime (dS4) possess infinitesimal symmetries generated by the conformal Killing vectors of dS4. However, it was later shown by Barnich, Bekaert, and Grigoriev that these theories are not invariant under the conformal algebra so(2, 4). To get some insight into these seemingly contradicting results we write down the full set of infinitesimal transformations of the fields generated by the fifteen conformal Killing vectors of dS4. In particular, although the infinitesimal transformations generated by the ten dS Killing vectors are well-known (these correspond to the conventional Lie derivatives), the transformations generated by the five non-Killing conformal Killing vectors were absent from the literature, and we show that they have an ‘unconventional’ form. In the spin-2 case (partially massless graviton), we show that the field equations and the action are invariant under the unconventional conformal transformations. For spin s > 2, the invariance is demonstrated only at the level of the field equations. For all spins s ≥ 2, we reproduce the result that the symmetry algebra does not close on the conformal algebra, so(2, 4). This is due to the appearance of new higher-derivative symmetry transformations in the commutator of two unconventional conformal transformations. Our results concerning the closure of the full symmetry algebra are inconclusive. Then we shift focus to the question of supersymmetry (SUSY) on dS4 and our objective is twofold. First, we uncover a non-interacting supermultiplet that consists of a complex partially massless spin-2 field and a complex spin-3/2 field on dS4. Second, we showcase the appearance of the unconventional conformal symmetries in the commutator of two SUSY transformations. Thus, this commutator closes on an algebra that is neither so(1, 4) nor so(2, 4), while its full structure is an open question. More open questions arising from our findings are also discussed.

show abstract

(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.

View full text Add to dashboard Cite

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.

show abstract

Notes on gauge fields and discrete series representations in de Sitter spacetimes

Cited by 3 publications

References 98 publications

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

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

Unconventional conformal invariance of maximal depth partially massless fields on dS4 and its relation to complex partially massless SUSY

(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

Contact Info

Product

Resources

About