Higher Spin de Sitter Hilbert Space

Anninos, Dionysios; Denef, Frederik; Monten, Ruben; Sun, Zimo

doi:10.48550/arxiv.1711.10037

Cited by 19 publications

(50 citation statements)

References 58 publications

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“…The notation on the LHS of (A.4) means we decompose the V |p i | -monomials there according to (A.3) omitting the y 1 • • • y k terms, and plug in the recurrence relations in the "x i − y i " terms. 18 We claim that (A.4) is manifestly satisfied. First, it is not difficult to see that the number of monomials in the vertex functions is the same on both sides.…”

Section: A Proof Of the Recurrence Relationmentioning

confidence: 87%

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Scalar Correlators in Bosonic Chern-Simons Vector Models

Yacoby¹

2018

Preprint

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We consider the planar limit of Chern-Simons theories coupled to a scalar φ in the fundamental representation of a U (N ) k gauge group, at both the regular and Wilson-Fisher conformal points. These theories have one single-trace scalar operator J 0 = φφ. We calculate its connected planar n-point functions, when all the external momenta are collinear. More specifically, we derive an algebraic recurrence relation that expresses each such n-point function in terms of lower-point ones. As an application, we study the four-point function, which was recently shown to be completely fixed up to three truncated solutions to the conformal bootstrap. We show that those truncated solutions do not contribute in our bosonic Chern-Simons theories. The result matches a recent calculation of the four-point function in Chern-Simons theories coupled to a fermion, providing a new test of 3d bosonization duality.

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Section: A Proof Of the Recurrence Relationmentioning

confidence: 87%

“…The result of the recurrence relation can be written in terms of the free scalar four-point 14 See [18] for a recent calculation of the integral (4.12).…”

Section: Four-pointmentioning

confidence: 99%

Scalar Correlators in Bosonic Chern-Simons Vector Models

Yacoby¹

2018

Preprint

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“…It would be very interesting to explore more uncharted territory and use theoretical consistency to map out the broader landscape of allowed field theories in de Sitter space. Clear targets are to understand (broken) supersymmetry and the viability of Vasiliev-like theories [75,114] from this bootstrap perspective. Beyond this, it would also be interesting to constrain the interactions of partially massless fields.…”

Section: Discussionmentioning

confidence: 99%

“…Operators can be mapped to their shadows by means of the shadow transform, which consists of convolving an operator with the two-point function of its shadow. See, for example, Appendix A of [75] for details.…”

Section: Symmetries and Ward Identitiesmentioning

confidence: 99%

The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization

Baumann,

Pueyo,

Joyce

et al. 2020

Preprint

115

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We extend the cosmological bootstrap to correlators involving massless particles with spin. In de Sitter space, these correlators are constrained both by symmetries and by locality. In particular, the de Sitter isometries become conformal symmetries on the future boundary of the spacetime, which are reflected in a set of Ward identities that the boundary correlators must satisfy. We solve these Ward identities by acting with weight-shifting operators on scalar seed solutions. Using this weight-shifting approach, we derive three-and four-point correlators of massless spin-1 and spin-2 fields with conformally coupled scalars. Four-point functions arising from tree-level exchange are singular in particular kinematic configurations, and the coefficients of these singularities satisfy certain factorization properties. We show that in many cases these factorization limits fix the structure of the correlators uniquely, without having to solve the conformal Ward identities. The additional constraint of locality for massless spinning particles manifests itself as current conservation on the boundary. We find that the four-point functions only satisfy current conservation if the s, t, and u-channels are related to each other, leading to nontrivial constraints on the couplings between the conserved currents and other operators in the theory. For spin-1 currents this implies charge conservation, while for spin-2 currents we recover the equivalence principle from a purely boundary perspective. For multiple spin-1 fields, we recover the structure of Yang-Mills theory. Finally, we apply our methods to slow-roll inflation and derive a few phenomenologically relevant scalar-tensor three-point functions.

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“…These operators generate equivalent representations of the conformal group and can be mapped to each other by means of the shadow transform. For scalar operators in momentum space, the shadow transform is implemented by the map [72] for more details.…”

Section: Spin-raising Operatormentioning

confidence: 99%

The Cosmological Bootstrap: Weight-Shifting Operators and Scalar Seeds

Baumann,

Pueyo,

Joyce

et al. 2019

Preprint

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A key insight of the bootstrap approach to cosmological correlations is the fact that all correlators of slow-roll inflation can be reduced to a unique building block-the four-point function of conformally coupled scalars, arising from the exchange of a massive scalar. Correlators corresponding to the exchange of particles with spin are then obtained by applying a spin-raising operator to the scalar-exchange solution. Similarly, the correlators of massless external fields can be derived by acting with a suitable weight-raising operator. In this paper, we present a systematic and highly streamlined derivation of these operators (and their generalizations) using tools of conformal field theory. Our results greatly simplify the theoretical foundations of the cosmological bootstrap program.

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Higher Spin de Sitter Hilbert Space

Cited by 19 publications

References 58 publications

Scalar Correlators in Bosonic Chern-Simons Vector Models

Scalar Correlators in Bosonic Chern-Simons Vector Models

The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization

The Cosmological Bootstrap: Weight-Shifting Operators and Scalar Seeds

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