Quantum Breaking Bound on de Sitter and Swampland
  Quantum consistency suggests that any de Sitter patch that lasts a number of
Hubble times that exceeds its Gibbons-Hawking entropy divided by the number of
light particle species suffers an effect of quantum breaking. Inclusion of
other interactions makes the quantum break-time shorter. The requirement that
this must not happen puts severe constraints on scalar potentials, essentially
suppressing the self-reproduction regimes. In particular, it eliminates both
local and global minima with positive energy densities and imposes a general
upper bound on the number of e-foldings in any given Hubble patch.
Consequently, maxima and other tachyonic directions must be curved stronger
than the corresponding Hubble parameter. We show that the key relations of the
recently-proposed de Sitter swampland conjecture follow from the de Sitter
quantum breaking bound. We give a general derivation and also illustrate this
on a concrete example of $D$-brane inflation. We can say that string theory as
a consistent theory of quantum gravity nullifies a positive vacuum energy in
self-defense against quantum breaking.
