Freezing Swampland: A Krylov Complexity Criterion for the Weak Gravity Conjecture

Abstract:We propose a quantum-information-theoretic perspective on the Weak Gravity Conjecture through the behavior of Krylov spread complexity. For a charged thermofield double state holographically dual to an AdS Reissner--Nordström black hole, we show that the extremal limit on the black-hole side is accompanied by an effective freezing of Krylov spreading. In this regime, the return amplitude becomes effectively a pure phase, and the dual quantum state ceases to spread nontrivially in Krylov space. We then incorporate charged matter and study the effect of Schwinger pair production in the near-horizon region. Within this semiclassical near-extremal analysis, the frozen behavior is lifted once the discharge channel is opened, and the dynamics become nontrivial again. This suggests that the Weak Gravity Conjecture may admit a complexity-based interpretation in terms of the absence of exact freezing in the presence of an available discharge channel. More broadly, our results point to a new connection between the swampland program, black-hole physics, and quantum information theory.

arXiv:2607.23747 [hep-th]

(or arXiv:2607.23747v1 [hep-th] for this version)

https://doi.org/10.48550/arXiv.2607.23747 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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