We present strong evidence that the tree level slow roll bounds of
arXiv:1807.05193 and arXiv:1810.05506 are valid, even when the tachyon has
overlap with the volume of the cycle wrapped by the orientifold. This extends
our previous results in the volume-dilaton subspace to a semi-universal
modulus. Emboldened by this and other observations, we investigate what it
means to have a bound on (generalized) slow roll in a multi-field landscape. We
argue that for any point ϕ0 in an N-dimensional field space with
V(ϕ0)>0, there exists a path of monotonically decreasing potential
energy to a point ϕ1 within a path length ≲O(1), such
that NlnV(ϕ0)V(ϕ1)≲−O(1). The
previous de Sitter swampland bounds are specific ways to realize this stringent
non-local constraint on field space, but we show that it also incorporates (for
example) the scenario where both slow roll parameters are intermediate-valued
and the Universe undergoes a small number of e-folds, as in the Type IIA set up
of arXiv:1310.8300. Our observations are in the context of tree level
constructions, so we take the conservative viewpoint that it is a
characterization of the classical "boundary" of the string landscape. To
emphasize this, we argue that these bounds can be viewed as a type of
Dine-Seiberg statement.Comment: v4: one more referenc