QFT and Topology in Two Dimensions: $$\mathrm{SL}(2, {{\mathbb {R}}})$$ SL ( 2 , R ) -Symmetry and the de Sitter Universe
Annales Henri Poincaré(2021)
摘要
We study bosonic quantum field theory on the double covering
$$\widetilde{dS}_{2}$$
of the two-dimensional de Sitter universe, identified to a coset space of the group
$$\mathrm{SL}(2, {{\mathbb {R}}})$$
. 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
$$\mathrm{SL}(2, {{\mathbb {R}}})$$
-invariant 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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