Abstract
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 ≲ mathcal{O} (1), such that sqrt{N} ln frac{Vleft({phi}_1right)}{Vleft({phi}_0right)}lesssim -mathcal{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.
Highlights
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
Oa(p1a),thsuocfhmthoantot√onNiclanllVVy((φφd10e))crea−siOng(1p)o. tTenhteiaplreenveiorguys to de Sitter swampland bounds are specific ways to realize this stringent non-local constraint on field space, but we show that it incorporates 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
We expect that our statements should hold for either all UV complete theories or at the very least for those UV complete theories that are at the classical limit of the moduli space
Summary
The statement of [66] (see [72]) is a statement about the (magnitude of the) slope of the potential. The argument generalizes previous No-Go statements in the literature [73] into a general principle As it stands this statement has counter-examples [67, 74] in tree level type II flux compactifications, where solutions with zero slope at positive values of the potential have already been constructed (see, e.g., [75,76,77,78]). The key point, we will see, is that unlike in other scenarios, the direction of the O(1) fall in the potential does not overlap with any of the elementary field directions and is fairly non-trivial to find Another interesting feature of this class of solutio√ns is that the field space is 14-dimensional, and we can clearly see the relevance of the N in making sure that the bound is satisfied. It should be noted that even though we believe the evidence we present is strong, it is based on “experimental data” from considerations of known tree level constructions in the literature
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