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A Walk Through Spin(1,d+1)
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A Walk Through Spin(1,d+1)
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We construct unitary irreducible representation of the de Sitter group, that forms the basis for the study of $dS_{d+1}$ QFT. Using the intertwining kernel analysis, we discuss bosonic symmetric tensor, and fermionic higher-spinors. Particular care is given to the structure and construction of exceptional series and fermionic operators. We discuss the discrete series, and explain how and why the exceptional series give rise to seemingly non-invariant correlators in de Sitter. Using tools from Clifford analysis, we show that for $d>3$, there are no exceptional fermionic representations, and so no unitary (higher)-gravitino fields. We also consider the structure of representations for $d=3$ and $d=2$, as relevant for the study of $dS_4$, the only space allowing for unitary gravitino and its generalisation, and of $dS_3$.
Forward citations
Cited by 5 Pith papers
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Ising the way into de Sitter
The two-dimensional thermal Ising model on de Sitter provides exact cosmological correlators that stay finite at late times, with perturbative secular logarithms resummed into principal-series oscillations.
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CFTs on Squashed Spheres and the Thermal Effective Action
Derives universal quadratic response of 3D CFT free energy to S^3 squashing proportional to c_T and constructs thermal effective action for high-T Seifert manifolds with explicit Wilson coefficients.
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Both Δ=1 and Δ=2 late-time Maxwell operators on planar dS4 furnish the photon unitary discrete series of SO(4,1), which splits into opposite-helicity summands via self-dual field-strength sectors.
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Revealing the conformal symmetry of the discrete series scalars in dS${}_2$
Massive discrete-series scalars in dS2 admit an on-shell global conformal symmetry realized non-locally on the scalar and locally on a conformal Killing tensor, with a traceless stress tensor generating SL(2,R)×SL(2,R).
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De Sitter Representations
Review of so(1,D) representations for de Sitter space across all D, covering mixed symmetry and fermions, connected to propagating fields.
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