REVIEW 9 cited by
A note on the representations of $\text{SO}(1,d+1)$
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
$\text{SO}(1, d+1)$ is the isometry group of $(d+1)$-dimensional de Sitter spacetime $\text{dS}_{d+1}$ and the conformal group of $\mathbb{R}^{d}$. This note gives a pedagogical introduction to the representation theory of $\text{SO}(1, d+1)$, from the perspective of de Sitter quantum field theory and using tools from conformal field theory. Topics include (1) the construction and classification of all unitary irreducible representations (UIRs) of $\text{SO}(1,2)$ and $\text{SL}(2,\mathbb R)$, (2) the construction and classification of all UIRs of $\text{SO}(1,d+1)$ that describe integer-spin fields in $\text{dS}_{d+1}$, (3) a physical framework for understanding these UIRs, (4) the definition and derivation of Harish-Chandra group characters of $\text{SO}(1,d+1)$, and (5) a comparison between UIRs of $\text{SO}(1, d+1)$ and $\text{SO}(2,d)$.
Forward citations
Cited by 9 Pith papers
-
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.
-
A Partially Massless Superconductor
A covariant Higgs mechanism turns the partially massless graviton into a fully massive spin-2 field by condensing a fractonic matter field with dipole symmetry.
-
Comments on holographic spread complexity
The momentum–spread-complexity relation requires generalized coherent states adapted to the spacetime symmetry algebra; semiclassical spreading alone cannot produce a momentum–complexity correspondence.
-
On the spectra of holographic QFTs on constant curvature manifolds
For holographic QFTs on constant-curvature manifolds, the spectrum is always discrete for negative curvature and always has a continuous component starting at m^2 = (9/4)α^{-2} for positive curvature.
-
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).
-
Microstate counting from defects in de Sitter
Counting defect microstates via Lorentzian wormholes reproduces the de Sitter and Schwarzschild-de Sitter entropy area laws.
-
4D de Sitter from 6D gauged supergravity with Green-Schwarz counterterm
6D gauged supergravity with the Green-Schwarz counterterm admits exact dS4×S2 and Mink4×S2 solutions (with a monopole); the de Sitter vacuum has two tachyons and flows to Minkowski.
-
Cosmological correlators in gravitationally-constrained de Sitter states
Cosmological correlators in gravitationally constrained de Sitter states are conformally invariant and differ from QFT vacuum correlators, but relational observables with a heavy background state can reproduce QFT results.
-
Lectures on Carrollian Holography
Massless scattering amplitudes, including gravitons, can be recast as correlators of a carrollian conformal field theory on null infinity, but the non-perturbative bootstrap program remains incomplete.
Discussion (0). Sign in to comment.