De Sitter Invariant Vacuum States, Vertex Operators, and Conformal Field Theory Correlators

Abstract

We show that there is only one physically acceptable vacuum state for quantum fields in de Sitter space-time which is left invariant under the action of the de Sitter-Lorentz group $SO(1,d)$ and supply its physical interpretation in terms of the Poincare invariant quantum field theory (QFT) on one dimension higher Minkowski spacetime. We compute correlation functions of the generalized vertex operator $:e^{i\hat{S}(x)}:$, where $\hat{S}(x)$ is a massless scalar field, on the $d$-dimensional de Sitter space and demonstrate that their limiting values at timelike infinities on de Sitter space reproduce correlation functions in $(d-1)$-dimensional Euclidean conformal field theory (CFT) on $S^{d-1}$ for scalar operators with arbitrary real conformal dimensions. We also compute correlation functions for a vertex operator $e^{i\hat{S}(u)}$ on the Łobaczewski space and find that they also reproduce correlation functions of the same CFT. The massless field $\hat{S}(u)$ is the nonlocal transform of the massless field $\hat{S}(x)$ on de Sitter space introduced by one of us.

14 pages, LaTeX file We thank Roman Jackiw for bringing to our attention Ref. 16

References in corpus (33)

• Relationship between Hawking Radiation and Gravitational Anomalies
• Anomalies, Hawking Radiations and Regularity in Rotating Black Holes
• Hawking Radiation from Charged Black Holes via Gauge and Gravitational Anomalies
• Hawking Radiation from Rotating Black Holes and Gravitational Anomalies
• Hawking radiation from dilatonic black holes via anomalies
• Hawking radiation from rotating black holes in anti-de Sitter spaces via gauge and gravitational anomalies
• Hawking Radiation and Covariant Anomalies
• Connecting anomaly and tunneling methods for Hawking effect through chirality
• Comments on anomaly versus WKB/tunneling methods for calculating Unruh radiation
• Hawking Radiation from General Kerr-(anti)de Sitter Black Holes
• Gauge and Gravitational Anomalies and Hawking Radiation of Rotating BTZ Black Holes
• Hawking Radiation, Effective Actions and Covariant Boundary Conditions
• Quantum Anomalies at Horizon and Hawking Radiations in Myers-Perry Black Holes
• Gravitational Anomalies, Hawking Radiation, and Spherically Symmetric Black Holes
• Anomalies of the Achucarro-Ortiz black hole
• Anomalies and de Sitter radiation from the generic black holes in de Sitter spaces
• Higher-spin Currents and Thermal Flux from Hawking Radiation
• Covariant anomalies and Hawking radiation from charged rotating black strings in anti-de Sitter spacetimes
• Fluxes of Higher-spin Currents and Hawking Radiations from Charged Black Holes
• Hawking radiation in GHS and non-extremal D1-D5 blackhole via covariant anomalies
• On Hawking radiation from black rings
• Hawking Radiation via Higher-spin Gauge Anomalies
• Anomaly Analysis of Hawking Radiation from Acoustic Black Hole
• Hawking Radiation via Gravitational Anomalies in Non-spherical Topologies
• Hawking radiation of a vector field and gravitational anomalies
• Hawking Radiation of Black Rings from Anomalies
• Hawking-Page Phase Transition of black Dp-branes and R-charged black holes with an IR Cutoff
• Ward Identities in the Derivation of Hawking Radiation from Anomalies
• Hawking radiation via anomaly cancelation for the black holes of five-dimensional minimal gauged supergravity
• Hawking fluxes, Fermionic currents, W(1+infinity) algebra and anomalies
• Hawking Radiation of Black p-Branes from Gravitational Anomaly
• Hawking Radiation and Quantum Anomaly in AdS2/CFT1 Correspondence
• A New Proof of Existence of a Bound State in the Quantum Coulomb Field

Cited by in corpus (3)

• Conformal Invariance, Dark Energy, and CMB Non-Gaussianity
• De Sitter and Schwarzschild-De Sitter According to Schwarzschild and De Sitter
• Orbifold Physics and de Sitter Spacetime