Taxonomy of branes in infinite distance limits
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When parameters become extreme in quantum gravity, the Emergent String Conjecture posits that either compact extra dimensions become large, or fundamental strings become tensionless. In this talk, I will argue that this conjecture requires various "taxonomy-rules" that theories of quantum gravity must satisfy. In particular, in asymptotic limits of moduli spaces of string vacua, I will argue that moduli-gradients of logarithms of brane and particle tensions are lattice-valued and satisfy various rules. In certain contexts, I will argue that these rules have only a finite and classifiable set of solutions, and that these solutions reproduce many non-trivial structures observed in string theory. These taxonomy rules might also predict new branes, such as branes with D-brane-like tensions in heterotic string theory, as well as strings in the Dark Dimension scenario with mass scales at, or below, the twelfth-root of the cosmological constant in Planck units. Based on 2505.10615.