Swampland Conjectures for Strings and Membranes

TL;DR

This work extends the Swampland program to low-codimension objects in 4d ${\cal N}=1$ EFTs by treating fundamental strings and membranes as localised EFT operators whose backreaction induces classical RG flows of their couplings. It shows that no-force identities derived from supersymmetry link the brane tensions and charges to the axionic kinetic terms and scalar potential, enabling a unified reading of WGC, SDC, and the de Sitter conjecture via these objects. A central output is that WGC for strings implies the Swampland Distance Conjecture with a universal exponential rate fixed by the string extremality, while WGC-saturating membranes yield potentials that satisfy the asymptotic de Sitter bound; together with a Distant Axionic String Conjecture, these results weave a coherent circle of Swampland constraints in 4d EFTs. The framework relies on an EFT flux lattice ${\Gamma}_{\rm EFT}$, Nilpotent Orbit data for asymptotic limits, and a dual 2-form/3-form description that makes the relevant kinetics and potential terms explicit. The findings provide a concrete, quantitative bridge between the geometry of moduli space, the dynamics of extended objects, and landscape/tandem swampland criteria with potential phenomenological implications for inflation and vacuum structure in ${\cal N}=1$ theories.

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 $\frac12$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.

Figures (9)

• Figure 1: A membrane inducing a jump on the fluxes, thus modifying the potential in the different regions separated by the membrane.
• Figure 2: The flux lattices as determined by the energy scales.
• Figure 3: A generating membrane interpolates between a fluxless configuration and a background with flux f, with a potential $V = \frac{1}{2} \mathcal{Q}^2_{\bf f}$ for the latter.
• Figure 4: Extremal region for mutually BPS (left) and non-mutually BPS states (right).
• Figure 5: The charge-to-tension ratios of BPS strings in a two modulus limit with $n_1=2$ and $n_2=3$, i.e. $K=-\log (s_1^2 s_2)$. To the left it is plotted the charge-to-tension vectors \ref{['strex_vecz']}, which draw a straight line independent of the cut-off $\Lambda$. To the right it is plotted the charge-to-tension ratio as we move along the flow, which is lower bounded by the extremality factor \ref{['gaminex']}.