We as humans let people get away with a lot of things, but cheating isn't something that you should compromise with. Not a man, nor a woman should ever deal with cheating and should confront their partners immediately. Love is a tunnel that opens at both ends and if you have been giving your wife the kind of love she deserves, then you should receive the love and loyalty yourself.
There is no problem with you loving your cheating wife, but if you aren't doing something about it, she might just take that to her advantage and continue with her affiar. So you should try to give her a second chance to see if she returns back to you and gets rid of the new man in her life. You should understand that sometimes we don't pay attention to our partners which is why they go astray. So if she is supposed to be blamed, you are supposed to be blamed to a certain degree yourself.
Try to talk to her as much as possible and find out where you went wrong. Ask her if you hurt her feelings in anyway. Try to get her back to you, but if she doesn't return back to you, leave her immediately or else you might cause yourself some serious trouble. I've seen people ruining their lives just because of a cheating partner and i don't want the same to happen to you. In such a scenario, moving on with life is the only option you've got, so just move on. Don't try to fight, argue or get phyrical with your wife and act mature, although it's tough not to do so. One fine day, she will realize how great a man you are and will want to come back to you, but you should still not accept her in anyway.