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I consider flat slices of moduli spaces where the (–∇ log T)-vectors of particle-towers and branes are constant, and I show that the Emergent String Conjecture constrains these vectors to reside on lattices. In asymptotic limits, this results in exponentially separated, discretized hierarchies of energy scales. I further identify conditions that determine whether a given lattice site must be populated, and I show that only a finite set of configurations satisfies these conditions. I classify all such configurations for 0d, 1d, and 2d moduli spaces in theories with 3 to 11 spacetime dimensions, and I argue that 11d is the maximal spacetime dimension compatible with my assumptions. Remarkably, this classification reproduces the detailed particle and brane content of various string theory examples with 32, 16, and 8 supercharges. It also describes some examples where the assumptions I use are violated, suggesting that my assumptions can be relaxed and the scope of this classification can be expanded. It might also predict new branes. For instance, if heterotic string theory is described by this classification, then it must possess non-BPS branes with D-brane-like tensions. Similarly, if this classification applies to the Dark Dimension Scenario with an extra modulus, then it requires the existence of strings with tensions related to the cosmological constant by T ≲ Λ^(1/6) in 4d Planck units.
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This content will become publicly available on March 1, 2026
Taxonomy of infinite distance limits
The Emergent String Conjecture constrains the possible types of light towers in infinite-distance limits in quantum gravity moduli spaces. In this paper, we use these constraints to restrict the geometry of the scalar charge-to-mass vectors -∇ log m of the light towers and the analogous vector -∇ log Λ of the species scale. We derive taxonomic rules that these vectors must satisfy in each duality frame. Under certain assumptions, this allows us to classify the ways in which different duality frames can fit together globally in the moduli space in terms of a finite list of polytopes. Many of these polytopes arise in known string theory compactifications, while others suggest either undiscovered corners of the landscape or new swampland constraints.
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- PAR ID:
- 10616746
- Publisher / Repository:
- Springer, SISSA
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2025
- Issue:
- 3
- ISSN:
- 1029-8479
- Page Range / eLocation ID:
- 213
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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