It would depend on so many things. Like:
1) How long it had been going on for: The longer the worse
2) Who I found it out from: Did I find out about it from her, or a friend, or a neighbor, or all by myself? The more socially distant the person, the more concerned I'd be. It would imply she hadn't been just lying to me about it, but everyone else around me as well. Different people have different positions on this, but this is mine.
3) Who she did it with: Complete stranger / random hookup through the internet, or an older friend of hers? If it was a complete stranger / random hookup, it tells me she might have something fundamentally wrong with her personality. Like, seriously. Reckless promiscuity is a underlying personality trait for sociopaths for example.
4) How many people did she do it with: no comment necessary
5) Why she did it: Did she do it for 'fun', or was she desperate for some reason?
6) What is her history like: Did she have a reputation for this sort of behavior, before we met?
7) My own 'situation' in life: a) Did my own work/life balance sabotage the relationship?
b) Was I being 'distant'? I know I can be.
c) Was she going through something else, and felt I was ignoring her?
If the the answer to any of those in 7 is 'yes', I'd consider holding on to her, though it would still be her job I think to say something about it first, instead of running off and sleeping with other guys.
8) How she reacted when I found out: Did she take responsibility, or did she instead get defensive about it? Did she start making up excuses, listing her alibis, and gaslighting me? I obliterate gaslighters. Nobody messes with my mind and gets to hang around me, and I make sure people know this in advance. I've gone 'no contact' with a large portion of my family over this already, and even distanced myself from entire groups of friends if it meant reducing the risk of running into such people again. If I can get them ostricised from the group, I do that as well. It's not a power game or revenge to me. I just literally don't want toxic people anywhere near me or my friends if I can do anything about it. That's only happened once in that context. And to a secretary in my undergrad uni (in a non-relationship context). And there's this extroverted girl at work who gaslighted me once when I was starting out in my career and we were working together, and now whenever I am around I can tell how nervous she gets, even nearly 2 years later. I can tell her confidence absolutely plummets when I'm in the room, and that's without me ever even saying a word to her about any of this, because she knows what she did, and that it did absolutely nothing to stop me.
Good.
Apologies if the rant at the end went off tangent. Boring day. To summarise it, do not tolerate gaslighters.
https://www.reddit.com/r/explainlikeimfive/comments/a5p2ca/eli5_what_is_gaslighting_and_some_examples/