Quantum three-dimensional de Sitter space

Abstract

We compute the canonical partition function of 2+1 dimensional de Sitter space using the Euclidean SU (2) × SU (2) Chern-Simons formulation of 3d gravity with a positive cosmological constant. Firstly, we point out that one can work with a ChernSimons theory with level k = l/4G, and its representations are therefore unitary for integer values of k. We then compute explicitly the partition function using the standard character formulae for SU (2) WZW theory and find agreement, in the large k limit, with the semiclassical result. Finally, we note that the de Sitter entropy can also be obtained as the degeneracy of states of representations of a Virasoro algebra with c = 3l/2G.

Multi-black-hole sectors ofAdS3gravity

“…For a negative cosmological constant there are black hole solutions [1,2], and the Bekenstein-Hawking entropy of these BTZ black holes have been attributed to boundary degrees of freedom at the horizon [3,4], at infinity [5] or at any intermediate timelike surfaces [6].…”

Inflation and the dS/CFT Correspondence

“…A primary difficulty with the dS/CFT conjecture is the absence of any well-controlled example of a de Sitter solution to string theory (or other form of quantum gravity) in which concrete calculations are possible and the conjecture can be tested. There is no direct construction of the boundary field theory, although some general characteristics can be indirectly deduced such as the relation between conformal weights and particle masses and the absence 1 This conjecture followed related observations in [5][6][7][8][9][10][11][12][13][14][15][16][17], and was inspired by an analogy to related early [18] and modern [19][20][21] results obtained in AdS (anti-de Sitter space) . See also [22,23].…”

Higher Spins from Nambu–Chern–Simons Theory

“…This does not immediately descend to the group of volume-preserving diffeomorphisms SDiff(S 3 ) that we are interested in. 12 However, the relationship between them is known. The following result was originally proven by Ebin and Marsden in the context of geometric hydrodynamics: This theorem is perhaps most easily understood as the statement that the principal bundle Diff(M)/SDiff(M) is trivial, and may be identified with the space V (Moser's theorem [47]).…”

“…The lowest su(2) spin ( j α = 1) sector is certainly identical to ordinary Euclidean Einstein gravity in 3D de Sitter space [12]. To answer the question, we will follow Blencowe [3] and Campoleoni et al [30] and examine whether the linearised theory around de Sitter space has a higher spin interpretation.…”

“…The group SO(4) ∼ = SU (2)× SU (2)/Z 2 is the gauge group corresponding to the spin 2 sector. Truncating to this sector gives Euclidean gravity on 3D de Sitter space [12]; likewise, su(n) ⊕ su(n) CS theory describes (Euclidean de Sitter) higher spin gauge theory (see appendix C of [13]). The SDiff(S 3 ) NCS theory therefore also describes higher spins on Euclidean de Sitter space, which we verify by calculating the spectrum of perturbations around this vacuum using harmonic analysis.…”