Is there any well known study that links government debt to tax rates? I have been searching the literature for some time now and haven't found any.
More importantly, could government debt track tax rates?
Looking across countries, there is not much of a relationship.
The following chart is taken from the latest IMF World Economic Outlook database, comparing General Government Gross Debt as a percentage of GDP (you could look at net debt) and General Government Revenue as a percentage of GDP (which includes more than taxation) both in 2014.
The extreme debts are for Japan and Greece, while the extreme revenues are for Tuvalu, Kiribati, and Micronesia (foreign aid related), and Kuwait (oil revenues/taxes). Hong Kong, Brunei, and Saudi Arabia have small gross debts while Nigeria and Bangladesh have the lowest revenues. But even without these special cases the relationship is weak.
You could instead look at individual countries over time, but some of the relationship may be cyclical (either political or economic) as lower debt encourages lower future tax rates, but lower tax revenues can lead to higher future debt rates.
Of course the true relationship also involves government expenditure rates and GDP growth rates among other significant factors.