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

Abstract

We study bosonic Quantum Field Theory on the double covering ${\widetilde{dS}}_2$ of the 2-dimensional de Sitter universe, identified to a coset space of the group $SL(2,\mathbb{R})$. 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 $SL(2,\mathbb{R})$-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.

arXiv comment43 pages, 1 figure

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