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arXiv · 2002.12084

QFT and topology in two dimensions: $SL(2,{\Bbb R})$-symmetry and the de Sitter universe

Henri Epstein·Ugo Moschella
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Abstract

We study bosonic Quantum Field Theory on the double covering $\widetilde{dS}_{2}$ of the 2-dimensional de Sitter universe, identified to a coset space of the group $SL(2,{\Bbb R})$. The latter acts effectively on $\widetilde{dS}_{2}$ and can be interpreted as it relativity group. The manifold is locally identical to the standard the Sitter spacetime ${dS}_2$; it is globally hyperbolic, geodesically complete and an inertial observer sees exactly the same bifurcate Killing horizons as in the standard one-sheeted case. The different global Lorentzian structure causes however drastic differences between the two models. We classify all the $SL(2,{\Bbb R})$-inveriant two-point functions and show that: 1) there is no Hawking-Gibbons temperature; 2) there is no covariant field theory solving the Klein-Gordon equation with mass less than $1/2R$ , i.e. the complementary fields go away.

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Henri Epstein, Ugo Moschella. 2020-02-27. QFT and topology in two dimensions: $SL(2,{\Bbb R})$-symmetry and the de Sitter universe. https://doi.org/10.1007/s00023-021-01030-7

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