Baby universes in 2d and 4d theories of quantum gravity

Understand

The validity of the Coleman mechanism, which automatically tunes the fundamental constants, is examined in two-dimensional and four-dimensional quantum gravity theories.

• First, we consider two-dimensional Euclidean quantum gravity on orientable closed manifolds coupled to conformal matter of central charge $c \leq1$.
• The proper time Hamiltonian of this system is known to be written as a field theory of noncritical strings, which can also be viewed as a third quantization in two dimensions.
• By directly counting the number of random surfaces with various topologies, we find that the contribution of the baby universes is too small to realize the Coleman mechanism.