Wave function of Vasiliev's universe: A few slices thereof
Abstract
We study the partition function of the free Sp(N) conformal field theory (CFT) recently conjectured to be dual to asymptotically de Sitter higherspin gravity in four dimensions. We compute the partition function of this CFT on a round sphere as a function of a finite mass deformation, on a squashed sphere as a function of the squashing parameter, and on an S^{2}×S^{1} geometry as a function of the relative size of S^{2} and S^{1}. We find that the partition function is divergent at large negative mass in the first case, and for small S^{1} in the third case. It is globally peaked at zero squashing in the second case. Through the duality this partition function contains information about the wave function of the universe. We show that the divergence at small S^{1} occurs also in Einstein gravity if certain complex solutions are included, but the divergence in the mass parameter is new. We suggest an interpretation for this divergence as indicating an instability of de Sitter space in higherspin gravity, consistent with general arguments that de Sitter space cannot be stable in quantum gravity.
 Publication:

Physical Review D
 Pub Date:
 October 2013
 DOI:
 10.1103/PhysRevD.88.084049
 arXiv:
 arXiv:1207.5517
 Bibcode:
 2013PhRvD..88h4049A
 Keywords:

 11.25.Tq;
 04.50.h;
 11.15.q;
 Gauge/string duality;
 Higherdimensional gravity and other theories of gravity;
 Gauge field theories;
 High Energy Physics  Theory
 EPrint:
 30 pages plus appendices, 6 figures