Ex gf broke up with me a year ago and wants me back now, what would you do?

She broke up with me a year ago and i heard rumors that she cheated on me with a guy and a girl. Around thanksgiving she started talking to me and we have been talking again and hanging out. We have good chemistry, really great sex, and a lot of fun. On top of this shes been really good to me, not being too needy, giving me space, being understanding, and shes taken me out to her sorority parties and introduced me to her new friends and iv had a lot of fun. she told me one day that she did not have sex with a girl and that the girl was crazy and making a bunch of things up, and that she never cheated on me with the guy either. Now i dont know if its true or not true, because i dont trust anything she says. what im trying to figure out though is do i go forward with this, because we have great chemistry and we both have our own lives now (we were together for 4 years prior) and things arelooking a lot better. not to mention despite being with other people during our 1 year breakup I still felt like something was missing in my life. since weve been talking and being just friends (yet still hooking up) I feel like my life is whole again and I feel really good and balanced and at ease with myself. So I guess what would you do, keep talking to her because she makes you feel good and it feels right and shes been so good about everything, or just turn and run because its possible shes lying and really did cheat on me.

p.s. she broke up with me because she joined a sorority her 2nd year at school and i really didnt like the idea of it and our relationship just went really sour and i kind of made a few big mistakes like punching one of her guy friends in the face.