They should carry or not carry under precisely the same laws under which residents of the various states within which they operate may or may not carry. They are not police officers, but merely investigators of Federal crimes. If they are operating within Chicago, for example, they should have to go about their business there unarmed like everyone else there does who's not a police officer recognized by that city. In Alaska or Vermont, they can carry any way they like at any time, etc., etc.,. The Constitution doesn't authorize a national police force, and what the Constitution doesn't authorize, it prohibits in accordance with the 10th Amendment.
