Your answer refers to the theoretical outputs of each of those - in which case capitalism also likewise probably does not result in slavery either? That's extremely highly debatable ofc and depends on whether we are talking about unregulated capitalism, which at that point might be better called anarchy, vs. a regulated form, which no longer produces actual slavery, bc of the regulations holding it back - and if the source of the regulations is a voting citizenry, then making it more akin to socialism even? (Bc despite the lack of direct ownership, they would have that indirect source of control - in theory at least.)

True anarchy does not produce slavery ofc. At least not in theoretical models, where once you enter a state you are never allowed to leave it. However, if you had a true anarchist state irl, then people would be free to do as they please. And since some people prefer to own slaves, therefore they would. And then more and more would, progressing through stages such as feudalistic warlords, which could no longer properly be called "anarchy" but it would bring us back to slavery at an institutional level (with peasants having no rights). Not just in theory but bc of actual practice in fact. Anarchy removes the institutional blockers to allow people to do as they wish, so seems to always be a temporary condition on the way towards something else that will last? Barring some external factors that can keep that going, like a small area in-between two large states that gets left alone so that it can be a buffer zone. Even a pirate kingdom will eventually become a feudal state with some people lording it over others, just bc they can (and bc their money or access to secret knowledge entices people to go along with it).

Outside of theory, irl I don't know that "capitalism" can exist without regulations keeping it going. Otherwise big monkey take from little monkey, and vice versa, without something (regulations) keeping that in check, so that monkey must exchange goods and services for money rather than simply bc they can get away with it. And ofc even "regulations" seems a simple word, but it too will have its nuances like a whole spectrum of how many and what type there are - e.g. are they only ever applied to the poors, in which case trending towards slavery but not bc of "capitalism" and rather bc of "anarchy" i.e. the lack of control of anyone stopping the rich from doing whatever they want.

And similarly, how could socialism exist irl either, without regulations propping it up? At which point I'll remind us that while regulated socialism doesn't lead to slavery, neither does regulated capitalism? But yes, unregulated capitalism can lead to slavery, and by a similar process, how could unregulated socialism not do the same? Bc "unregulated" anything really means anarchy, whatever it used to be before it lost its regulatory abilities.

i.e. these terms - capitalism, socialism, and anarchy - do not refer to systems, or at least not stable ones over time i.e. especially referring to those existing irl, but rather processes, that must be sustained (or else systems that maintain those processes). Bc the entropic decay process will counterbalance any such irl process by allowing anarchy to creep in and therefore trend towards slavery, hence an equal and opposing force must be applied to halt that shift. This leads to such extremely ironic - laughably so - thoughts such as: is the USA somehow not capitalist enough to prevent slavery (e.g. landlords need to provide goods and services in exchange for money, rather than simply collect in return for nothing), which I say is ironic bc capitalism always trends towards anarchy, as money acts to corrupt. However the crucially important distinction, i.e. the reason I went into that tangent, is that it is the lack of capitalism there that was the direct cause of the slavery, the latter being due rather to the anarchy, even while at the same time we all know that capitalism will eventually trend towards anarchy overall, ironically not bc it is too strong but bc it is too weak to resist that inevitable slide into anarchy.

And then the caveat is that socialism is the same way: it too irl has to fight that slide into anarchy and thereby feudalism and slavery. Its corrupting influences may not be monetary and instead other forms of power but the underlying greed is the same. A regulated capitalism can avoid slavery, for a time until it succumbs to anarchy, and a regulated socialism can do the same, until it too succumbs to anarchy as well. Maybe if can last longer? We have yet to see such proof irl, but maybe? But ultimately they both lead to slavery, unless efforts are expended to prevent that, at which point we must be fair to the truth and say that neither causes slavery directly, at least not while they are still actively maintained and haven't yet fallen into the anarchy state... but both have that pit of anarchy ready to swallow them up if not resisted, and yet irl both really do resist it, for a time as best they can.