My man is Texting another girl on facebook. Should I break up with him?

I just found out that my boyfriend has been texting this other girl that he never met face to face, but met on facebook. I looked trough his phone and they have been sending eachother naked photos and he thinnks that I don't know ****. Now we have been together for 6 years and he has two kids and I have none. I've been taking care of them and him too. I feel so disrepected. I got all this evidence and I want to break up, but I'm scared. Is this grounds for breaking up? The crazy thing about it is. They never met in person. Only on facebook.