QG Seminar (Zoom): The Boundary of Symmetric Moduli Spaces and the Distance Conjecture

The swampland distance conjecture (SDC), which states that at any boundary of moduli space a tower of states becomes exponentially massless, is widely believed to be a universal feature of quantum gravity and has passed numerous tests within string theory. Yet, despite its connections to other conjectures supported by bottom-up reasoning, the SDC itself currently lacks such an explanation. After reviewing the conjecture and its various formulations, I will show that, under mild assumptions, it is automatically satisfied in any effective theory whose moduli space is locally symmetric — a setting in which boundaries, geodesics, and spectra can be fully described using group-theoretic data. I will further explain how this formalism constrains effective field theories by requiring that towers of states become massless at infinte distance in a manner compatible with the decay rates of Kaluza–Klein and string excitations. This yields a concrete list of admissible duality groups and (single) irreducible particle representations consistent with these assumptions. Several of the resulting theories appear in the known landscape of string compactifications, while a handful remain to be realised, or shown to lie in the swampland. 

This talk is based on 2508.18401 and work in progress with S. Baines, B. Fraiman, M. Graña, and D. Waldram.