sooo… he cheated

if anyone remembers my last post here (i dont think so) i was doubting whether my bf had cheated or not (he DM’d another girl while we were on a break where we specified we wouldn’t talk to other ppl). Yesterday some friends told him my whole faculty was talking about it and saying him and the girl hooked up, he denied it many times only i finally got the truth out of him. He had sex with her but claims he doesn’t remember (yet he remembers details about it) Honestly i feel sick and even though i love him a lot i know i have to break up with him. please wish me luck and strength i think i’ll need it.