literally? By what definition? Are anarchist capitalists also authoritarian? In what way is Rand Paul actually authoritarian? Or are you just talking out of your ass?
Literally as in they are directly correlated and are synonyms for one another. The political compass works in such a way that if you turn it clockwise, you will have the social right on the right and the social left on the left.
This second point doesn't make any sense, there is no correlation to being a free-market capitalist and being socially libertarian, so I'll skip it.
Rand Paul is "authoritarian" in that he is 100% pro-life, prefers gay marriage to be decided by the states because he doesn't personally believe in it, is against drug legalization, and is for intervention in Syria.
He is "libertarian" in that he believes drug use should be
decriminalized, believes in gun rights, is against mandatory vaccinations, as well as believes the government should generally stay out of people's social and personal lives.
The mixture of these two is why he is not as far north as the other republican candidates but also why he's not as south as Ron Paul. He's not as much a libertarian as his pro-choice, pro-gay marriage, pro-legalization, and anti-war father, but he still is more than probably any other republican candidate.