Abstract
Swampland criteria like the Weak Gravity Conjecture should not only apply to particles, but also to other lower-codimension charged objects in 4d EFTs like strings and membranes. However, the description of the latter is in general subtle due to their large backreaction effects. In the context of 4d mathcal{N} = 1 EFTs, we consider frac{1}{2} BPS strings and membranes which are fundamental, in the sense that they cannot be resolved within the EFT regime. We argue that, if interpreted from the EFT viewpoint, the 4d backreaction of these objects translates into a classical RG flow of their couplings. Constraints on the UV charges and tensions get then translated to constraints on the axionic kinetic terms and scalar potential of the EFT. This uncovers new relations among the Swampland Conjectures, which become interconnected by the physical properties of low-codimension objects. In particular, using that string RG flows describe infinite field distance limits, we show that the WGC for strings implies the Swampland Distance Conjecture. Similarly, WGC-saturating membranes generate a scalar potential satisfying the de Sitter Conjecture.
Highlights
The Swampland program [1,2,3] aims at identifying universal criteria that any effective field theory (EFT) should satisfy to admit a UV embedding in a consistent theory of quantum gravity
Any generalisation of the Weak Gravity Conjecture (WGC) to low codimension objects [5, 7,8,9,10] usually involves dealing with probe branes, but a proper treatment taking into account their backreaction is missing
If the mass for the scalars is below the EFT cut-off Λ, there is a sublattice of fundamental membranes such that the anomaly can be cured at the EFT level, which is a non-trivial consistency check
Summary
The Swampland program [1,2,3] aims at identifying universal criteria that any effective field theory (EFT) should satisfy to admit a UV embedding in a consistent theory of quantum gravity. We review the description of these objects from the EFT viewpoint, and in particular the field-dependent expressions for their tensions and physical charges obtained in terms of dual effective actions. Such expressions directly lead to identities which, at least naively, can be interpreted as no-force conditions among extended objects of equal charge. As shown in [30], ΓEFT must be such that these pairings become linear after fixing the non-dynamical fluxes, a condition that can be made compatible with the definition (2.12) in typical string theory examples In this dual framework one can describe the action of a membrane with charges qa as. This observation will be central for the discussion of the section and crucial for the rest of the paper, as it will provide a vantage point to analyse swampland criteria
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