The debt:GDP ratio is a ratio. The numerator is the debt, and the denominator is the GDP. So countries that experience a growth slowdown will tend to see high debt:GDP ratios whereas fast-growing countries will see their debt:GDP ratio tumble.
Kenneth Rogoff sees this differently:
In a series of academic papers with Carmen Reinhart – including, most recently, joint work with Vincent Reinhart (“Debt Overhangs: Past and Present”) – we find that very high debt levels of 90% of GDP are a long-term secular drag on economic growth that often lasts for two decades or more. The cumulative costs can be stunning. The average high-debt episodes since 1800 last 23 years and are associated with a growth rate more than one percentage point below the rate typical for periods of lower debt levels. That is, after a quarter-century of high debt, income can be 25% lower than it would have been at normal growth rates.
But why does he see it his way? Inferences from statistical correlations to causal hypotheses are difficult to make. But my read of the meaning of the correlation has a clear mechanism. National governments go into debt frequently, and some indebted states suffer growth slowdowns that mechanically increase their debt:GDP ratio. By contrast through what mechanism do these high debt levels cause slow growth? Or think of it this way. Japan has the highest debt:GDP ratio in the world. A huge share of that debt is owed to Japanese households. If a new patriotic fad swept the country in which Japanese households tore up their bonds and relieved their government of its debt obligations, would Japanese GDP growth be supercharged? How? Why? It seems mysterious. By contrast it's obvious that if Japanese growth were to be supercharged that Japan's debt:GDP ratio would fall. How could it not?