To my understanding, specific geographic regions are always capitalized. For example, Southern US is proper because it is a specific region.
However, a co-author argues that southern should not be capitalized, because it is an adjective, not a noun.
So which is it? Southern US or southern US?
Per comment: Note that I am speaking of a particular region of the United States, not "a location in a particular sector." Hence, presumably, the portion of the United States known widely as the (S/s)outhern United States.