Political theory is one of the subfields of the Political Science Department. In general, "political theory" can mean one of two related things:
- Political philosophy: In which one might study, for example, Core Curriculum classics like Locke and Hobbes as well as more recent thinkers like John Rawls. Related areas of study include legal philosophy and moral philosophy. There's not much of this sort of political theory in the political science department -- you're more likely to encounter it in the philosophy department. Nevertheless, papers and even senior theses in political science do get written in this area from time to time.
- Formal theory: In which scholars attempt to develop mathematical models of political science phenomena, e.g. voting behavior (so-called "social choice theory"). This area of study is heavily inspired by the success of formal models in economics, and a lot of the major results are due to scholars like Kenneth Arrow who are known to the wider world primarily as economists. There's a lot of formal logic and math involved here, and many of its practitioners studied math at some point in their lives. (N.B.: formal theory is not the same thing as quantitative/statistics-based/empirical political science, though they are related).
Political theory is not listed as an available subfield on the Columbia College Bulletin, but political science majors can make it one of their subfields if they ask nicely.