Freezing Swampland: A Krylov Complexity Diagnostic 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 corresponding Krylov spread is suppressed. 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 an allowed discharge channel is opened, and the dynamics become nontrivial again. This suggests a possible complexity-based diagnostic of a characteristic physical consequence of the Weak Gravity Conjecture: the availability of a superextremal charged state that can mediate discharge. More broadly, our results point to a connection between the swampland program, black-hole physics, and quantum information theory.

arXiv comment27 pages