QFT and Topology in Two Dimensions: \mathrm{SL}(2, {{\mathbb {R}}})Symmetry and the de Sitter Universe
Abstract
We study bosonic Quantum Field Theory on the double covering $\widetilde{dS}_{2}$ of the 2dimensional 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 onesheeted case. The different global Lorentzian structure causes however drastic differences between the two models. We classify all the $SL(2,{\Bbb R})$inveriant twopoint functions and show that: 1) there is no HawkingGibbons temperature; 2) there is no covariant field theory solving the KleinGordon equation with mass less than $1/2R$ , i.e. the complementary fields go away.
 Publication:

Annales Henri Poincaré
 Pub Date:
 September 2021
 DOI:
 10.1007/s00023021010307
 arXiv:
 arXiv:2002.12084
 Bibcode:
 2021AnHP...22.2853E
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 43 pages, 1 figure