Tensors and Spinors in de Sitter Space

Pethybridge, Ben; Schaub, Vladimir

doi:10.48550/arxiv.2111.14899

Cited by 5 publications

(5 citation statements)

References 88 publications

(156 reference statements)

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“…The scalar case we are studying leaves only states with even action under this transformation. The odd states are relevant to the case of fermionic fields as considered in [110,111], to which our analysis can be extended. We note that the complementary series are non-unitary in the odd case, and so would not appear in the decomposition of the identity.…”

Section: Spectral Decomposition: a Proposalmentioning

confidence: 99%

The discreet charm of the discrete series in dS₂

Anninos,

Anous,

Pethybridge

et al. 2023

J. Phys. A: Math. Theor.

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We study quantum field theories placed on a two-dimensional de Sitter spacetime (dS2) with an eye on the group-theoretic organization of single and multi-particle states. We explore the distinguished role of the discrete series unitary irreducible representation (UIR) in the Hilbert space. By employing previous attempts to realize these states in free tachyonic scalar field theories, we propose how the discrete series may contribute to the Källén–Lehmann decomposition of an interacting scalar two-point function. We also study BF gauge theories withSL(N,R)gauge group in dS2and establish a relation between the discrete series UIRs and the operator content of these theories. Although present at the level of the operators, states carrying discrete series quantum numbers are projected out of the gauge-invariant Hilbert space. This projection is reminiscent of what happens for quantum field theories coupled to semiclassical de Sitter gravity, where we must project onto the subspace of de Sitter invariant states. We discuss how to impose the diffeomorphism constraints on local field-theory operators coupled to two-dimensional gravity in de Sitter, with particular emphasis on the role of contact terms. Finally, we discuss an SYK-type model with a random two-body interaction that encodes an infinite tower of discrete series operators. We speculate on its potential microscopic connection to theSL(N,R)BF theory in the large-Nlimit.

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Section: Spectral Decomposition: a Proposalmentioning

confidence: 99%

The discreet charm of the discrete series in dS₂

Anninos,

Anous,

Pethybridge

et al. 2023

J. Phys. A: Math. Theor.

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“…Finally, the last area in which this work can have an impact is quantum field theory in de Sitter space-time. Many recent works have exploited the Euclidean conformal symmetry of late-time correlators [47][48][49][50][51][52], but the Lorentzian conformal group also plays an important role in the in-in formalism recently put forward [53][54][55][56].…”

Section: Correlation Functionmentioning

confidence: 99%

Spinors and conformal correlators

Gillioz

2021

Preprint

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In conformal field theory, momentum eigenstates can be parameterized by a pair of real spinors, in terms of which special conformal transformations take a simpler form. This well-known fact allows to express 2-point functions of primary operators in the helicity basis, exposing the consequences of unitarity. What is less known is that the same pair of spinors can be used, together with a pair of scalar quantities, to parameterize 3-point functions. We develop this formalism in 3 dimensions and show that it provides a simple realization of the operator product expansion (OPE) for scalar primary operators acting on the vacuum.

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“…Recent reviews from the physics literature on the de Sitter group in general dimensions include [3] which focus on cases of integer spin, and in sections of [4] that focus on the scalar representations and how they manifest themselves at the late-time boundary. For the case of spinors we refer the readers to [5] and references within. Here we will mainly follow the in depth monologue [6].…”

Section: Introductionmentioning

confidence: 99%

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

Şengör¹

2022

Proceedings of Corfu Summer Institute 2021 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2021)

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Our main goal here is to provide an introduction on some of the well established properties of the representation theory of 𝑆𝑂 (𝑑 + 1, 1), for those considering to think on physical problems set in de Sitter space in terms of these representations. With this purpose we review two intertwining maps, the map 𝐺 that is used in constructing a well defined inner product for the complementary series representations and the map 𝑄 that is involved in constructing composite representations. We give explicit examples from the late-time boundary of de Sitter on the practical use of the complementary series inner product and in building a tensor product representation from unitary principal series irreducible representations.

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Tensors and Spinors in de Sitter Space

Cited by 5 publications

References 88 publications

The discreet charm of the discrete series in dS₂

The discreet charm of the discrete series in dS₂

Spinors and conformal correlators

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

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Tensors and Spinors in de Sitter Space

Cited by 5 publications

References 88 publications

The discreet charm of the discrete series in dS2

The discreet charm of the discrete series in dS2

Spinors and conformal correlators

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

Contact Info

Product

Resources

About

The discreet charm of the discrete series in dS₂

The discreet charm of the discrete series in dS₂