Not exactly.

It’s not that there’s little or no primary source evidence for Roman slavery. There’s a lot, in literature, in private letters, in contracts, in law compilations and juridical commentary, in artwork, in epigraphy (inscriptions, such as those on tombstones), and in countless snippets everywhere. It is difficult to find any sphere of Roman life not touched in some way by slavery.

The challenge is precisely that: the sources are in countless snippets everywhere, not in major texts dedicated to the topic of slavery. No Roman ever sat down to write a narrative history and exposition of slavery the way Thucydides did for the Peloponnesian War or Polybius did for the Punic Wars – or if one ever did, nobody bothered to copy and preserve the work. Few Roman writers (who almost all came from the upper ranks of society) ever cared to put lowly slaves in the foreground of the narratives they wrote about themselves.

But slaves are often present in the background, or foregrounded only for a few pages when an author briefly does have something to say about slaves and slavery, or so on. Historians of Roman slavery get much of the evidence by gleaning mentions of slavery from texts that are mostly concerned about other things. And we actually find these sorts of fleeting glimpses of slavery all over the place, which testifies to the ubiquitousness of slavery in Roman society.

For example, Augustine of Hippo (the Christian saint) happens to describe slave-raiding, specifically the depredations of Roman slave-traders, presumably displaced from their usual cross-frontier hunting grounds by the invasions and wars that would soon end the Empire in the west and tempted, considering the collapse of Roman authority, to prey on fellow Romans instead (https://wesleyscholar.com/wp-content/uploads/2019/04/Augustine-Letters-211-270.pdf starting on p. 263). This isn’t because Augustine felt generally inspired to record the nature of slave-raiding but because he saw that Roman slavers were preying semi-openly on other Romans and he was trying to raise the alarm and get help. It’s just one among hundreds of Augustine’s letters that are almost all about other topics.

In a previous answer here on AskHistorians I mentioned that in one of the Controversiae of Seneca the Elder (specifically, it’s 1.2), some of the speakers are confronted with the claim that a woman might have been enslaved, trafficked, and sold without having been raped along the way, and that they either outright disbelieve it as a ludicrous lie, or else argue that it is so unusual that it’s actually proof of a divine miracle having happened. That tells us something grim about enslavement – but that’s something we get from mining a couple pages out of a text about something completely different, namely a collection of sample rhetoric for a rhetorical education. Not exactly a primary source about slavery.

There’s an episode in Petronius’s novel Satyricon in which the comic heroes try to disguise themselves as slaves, part of which involves drawing fake branding marks on their faces. Just a snippet before the novel’s plot moves on to other things, but it’s a piece of evidence we can add to the pile for a Roman practice of punitive facial branding of slaves.

And so on. The upshot is, the primary-source information about slavery is scattered here and there in bits and pieces. I can’t give you any one primary source, or even any few primary sources, that will give you anything close to a complete picture.

What I’m going to recommend, then, even though you say you’re not looking for secondary sources, are secondary sources… to be mined as a means of getting at the primary sources. I mean, you could try to sort through the vast corpus of Roman literature yourself and collect these bits and pieces, but I don’t recommend it, since the work has been done by others!

A solid, academic secondary source on Roman slavery will at very least be full of footnotes or end notes that document which primary sources have been used. Better, some will actually directly quote numerous passages of interest from primary sources. Best, some will quote them in English translation instead of in untranslated Latin or Greek (which, unfortunately for casual readers, does tend to be a habit of some of the field’s less accessible secondary sources).

But I’m not sure where you fall on the spectrum of academic history literacy vs. pop history literacy, so I’m actually going to start out by recommending a book that is firmly on the pop-history side of the slider and probably a bit unusual by the standards of AskHistorians. It’s The Roman Guide to Slave Management by Jerry Toner.

The conceit of this book is that Toner writes in-character as a Roman aristocrat explaining various aspects of slavery (from, of course, the master’s and not the slave’s perspective, as the title suggests). It’s a creative enough schtick for a pop book, although you may find the in-character persona wearing a bit thin by the later chapters (I know I did). But that’s not why I’m mentioning it.

The book is organized such that Toner writes one chapter at a time talking about some aspect of Roman slavery in-character, each followed by an out-of-character commentary on what he’s just written. At the very end of each of these commentary sections are a couple paragraphs describing the sources he drew upon for the various things he has mentioned while writing in-character. It’s these paragraphs that I think you might find useful, because the sources he draws on skew heavily towards primary sources. They also tend to be usefully grouped by topic, as they will be sources that deal with the topic of his in-character chapter. These lists of (mostly) primary sources at the end of each commentary chapter seem like they might be just what you’re looking for.

However, if you’re comfortable with secondary sources that fall on the more academic side of the spectrum, let me know. Roman slavery has been a hot topic in academia in recent decades and I can point you to a number of less lightweight secondary sources that are nevertheless generous with their citing and quoting of the primary sources they draw on. If this sort of thing would be up your alley, it might also help to narrow down the topic a bit, because (for example), a secondary source dealing with the role of manumission and freedmen in the Roman slave system will point to a very different set of sources than one that focuses on, say, the role of slavery in the rural agricultural economy, which will point to different primary sources from one that focuses on the treatment of slavery in Roman legal theory and juridical writing, which will point to different primary sources from one that focuses on slavery in prostitution and the sex trade, and so on…