The paper does not report a link between low carb and AF in any way. It reports an association, but does not demonstrate cause or linkage at all or exclude other relevant factors. It's a very big "so what" from me.
The paper is weak because it datamines earlier data (beginning from the 1980s) rather than doing any of its own research: the data establishes "low-carbohydrate intake" through a self-report questionaire at the beginning of the process (ie in the 1980s). Self-report questionaires are a notably bad way to establish what the participants actually ate during the period of the study, rather than what they claimed to eat (particularly before it started) - there appears to be no information in the paper on what was eaten during the study at all, and the lack of it doesn't seem to bother the authors. It should.
Neither can I find anything in the paper that says how much carb was "low-carb" - it's only given as the percentage of overall energy derived from carb. This is important, because it means that the low carb group might not actually have been low carb at all, depending on what else they claimed to be eating in the 1980s.
The paper separates the study group into four quartiles: the lowest were getting 37.5 +/- 4.7% energy from carb (if the questionaire responses can be accpted as accurate) while the top quartile was on 60.8+/- 5.3%. Mean was 48.8 +/-9.8%. So (again if accurate) the "low carb" quartile was still getting around 40% of its energy from carb. That's not low carb as I understand it.
using percentages rather than actual amounts means that someone eating (say) 5,000 calories a day would be put in that "low-carb" group if 2,000 calories or less came from carb. So, even if accurate, it tells you exactly nothing about actual carb intake.
And the paper then says:
Participants with a relatively low percentage of energy from carbohydrate were more likely to be young, men, white, smokers, and ever drinkers; and to have diabetes mellitus, a high education level, a high high‐density lipoprotein cholesterol level, a high uric acid level, high total fat intake, high animal fat intake, high total protein intake, high animal protein intake, low plant protein intake, low dietary fiber intake, a low glycemic index, and a low glycemic load.
I would have thought that there are enough confounding possibilities in this group to make anyone cautious about assigning an "association" with AF to the 40% "energy from carb" factor alone. But it doesn't seem to have deterred the authors.