Two-dimensional dS/CFT correspondence

Abstract

We investigate de Sitter/conformal field theory (dS/CFT) correspondence in two dimensions. We define the conserved mass of de Sitter spacetime and formulate the correspondence along the lines of anti-de Sitter/conformal field theory duality. Asymptotic symmetry group, mass, and central charge of de Sitter spacetime are equal to those of anti-de Sitter spacetime. The entropy of two-dimensional de Sitter spacetime is evaluated by applying Cardy formula. We calculate the boundary correlators induced by the propagation of the dilaton in two-dimensional de Sitter space. Although the dilaton is a tachyonic perturbation in the bulk, boundary conformal correlators have positive dimension. *

Closed string tachyon condensation and worldsheet inflation

“…In two dimensions, this formula is rather ambiguous -the horizon of the static patch is a zero-dimensional sphere, which is only a pair of points; and one must identify the quantity playing the role of G, since there is no Einstein gravity per se. The two approaches [62] and [63,64,65] make differing assumptions, but both arrive in the end at expressions of the form…”

“…For example, the entanglement approach of [62] takes the point of view of a static observer, considering the entanglement of their observable degrees of freedom with those behind their horizon; energy and temperature are those measured by the static observer. On the other hand, the approach of [63,64,65] uses asymptotic symmetries on the spacelike slice at conformal infinity, and is thus necessarily observing the entire state. In particular, it is not clear how to relate the energies of the two approaches, nor is it clear what interpretation to give the entropy computed in [63,64,65].…”

“…On the other hand, the approach of [63,64,65] uses asymptotic symmetries on the spacelike slice at conformal infinity, and is thus necessarily observing the entire state. In particular, it is not clear how to relate the energies of the two approaches, nor is it clear what interpretation to give the entropy computed in [63,64,65]. 24 23 In the semiclassical limit, γ d−1…”

“…[61] for a review), gravitational entropy in de Sitter space has remained a bit more mysterious. There have been a number of analyses of the entropy of two-dimensional de Sitter space, for example using ideas of quantum entanglement [62], or considering topological gravity and its asymptotic symmetry algebra [63,64,65] (following the ideas of [66]). …”

TACHYONS IN DE SITTER SPACE AND ANALYTICAL CONTINUATION FROM dS/CFT TO AdS/CFT

“…[15] it was argued that a scalar particle with positive square-mass in dS space is like a tachyon in AdS space. Moreover, investigating the dS 2 /CFT 1 correspondence [16,17] along the lines of the AdS 2 /CFT 1 duality [18,19], it was shown that a tachyonic perturbation in the two-dimensional bulk corresponds to a boundary conformal operator of positive dimension. The key idea we use in this paper is very simple.…”