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arXiv · 2607.23747

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

Amin Faraji Astaneh·Reza Ghomi Shurkaie
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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--Nordstr\"om 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.

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Amin Faraji Astaneh, Reza Ghomi Shurkaie. 2026-07-26. Freezing Swampland: A Krylov Complexity Criterion for the Weak Gravity Conjecture. https://arxiv.org/abs/2607.23747

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