Holography in de Sitter and flat spacetimes

5 problems

• Is 4D flat-space gravity dual to a 3D Carrollian field theory?

  Open

  An alternative to the celestial sphere places the equivalent description of flat-space gravity on null infinity, the surface reached by outgoing light rays, as a theory in which the speed of light is effectively zero (a Carrollian theory). Whether such a theory exists with its own rules, independent of the gravity calculation, is unknown.

• Is there a consistent celestial CFT for four-dimensional gravity?

  Partially resolved

  Scattering of particles in flat space can be rewritten as correlations on a sphere at infinity. Whether these correlations form a self-consistent quantum theory on that sphere is unknown.

• Holographic dual of quantum gravity in de Sitter space

  Open

  A universe with positive vacuum energy has no spatial boundary to hold an equivalent quantum theory. Where such a description lives and what it is are unknown.

• Microscopic count of de Sitter horizon entropy

  Open

  The horizon of an expanding universe has an entropy proportional to its area, just like a black hole. Which quantum states it counts is unknown.

• Does the flat-space limit of AdS/CFT define the full S-matrix?

  Open

  Shrinking the curvature of anti-de Sitter space to zero should turn its exact boundary description into flat-space scattering. Whether this works beyond approximations is unknown.