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.
Related
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BibTeX
@misc{astaneh2026freezing,
title = {{Freezing Swampland: A Krylov Complexity Diagnostic for the Weak Gravity Conjecture}},
author = {Amin Faraji Astaneh and Reza Ghomi Shurkaie},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2607.23747},
eprint = {2607.23747},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.23747},
note = {CC0},
}
RIS
TY - UNPB
TI - Freezing Swampland: A Krylov Complexity Diagnostic for the Weak Gravity Conjecture
AU - Amin Faraji Astaneh
AU - Reza Ghomi Shurkaie
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2607.23747
UR - https://arxiv.org/abs/2607.23747
AB - 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.
ER -