Abstract
We consider spacetime-dependent solutions to string theory models with tadpoles for dynamical fields, arising from non-trivial scalar potentials. The solutions have necessarily finite extent in spacetime, and are capped off by boundaries at a finite distance, in a dynamical realization of the Cobordism Conjecture. We show that as the configuration approaches these cobordism walls of nothing, the scalar fields run off to infinite distance in moduli space, allowing to explore the implications of the Swampland Distance Conjecture. We uncover new interesting scaling relations linking the moduli space distance and the SDC tower scale to spacetime geometric quantities, such as the distance to the wall and the scalar curvature. We show that walls at which scalars remain at finite distance in moduli space correspond to domain walls separating different (but cobordant) theories/vacua; this still applies even if the scalars reach finite distance singularities in moduli space, such as conifold points.We illustrate our ideas with explicit examples in massive IIA theory, M-theory on CY threefolds, and 10d non-supersymmetric strings. In 4d mathcal{N} = 1 theories, our framework reproduces a recent proposal to explore the SDC using 4d string-like solutions.
Highlights
We illustrate our ideas with explicit examples in massive IIA theory, M-theory on CY threefolds, and 10d non-supersymmetric strings
We show that walls at which scalars remain at finite distance in moduli space correspond to domain walls separating different theories/vacua; this still applies even if the scalars reach finite distance singularities in moduli space, such as conifold points
When scalars remain at finite distance points in moduli space as one hits the wall, it corresponds to an interpolating domain wall, and the solution continues across it in spacetime;
Summary
Walls of nothing and infinite moduli space distance. we consider different kinds of cobordism walls in massive IIA theory [29], extending the analysis in [11]. According to the SDC, there is an infinite tower of states becoming massless in this region, with a scale decaying exponentially with the moduli space distance D as MSDC ∼ e−λD ,. We can write the SDC tower scale in terms of the scalar curvature as MSDC e−λD. This scaling is highly reminiscent of the Anti de Sitter Distance Conjecture (ADC) of [23],7 even though the setup under consideration is very different.. The point we would like to emphasize is that, since Z remains finite across them, the dilaton remains at finite distance in moduli space, as befits interpolating domain walls from our discussion in the introduction
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