Do I have a case

I recently quit my shift manager job at Arby's, due to complete humiliation. There was an ANONYMOUS rumor made that I was having a sexual relationship with one of my employees on the premasis. I was investigated and they found nothing, no solid proof that I did anything sexual with that employee, all they had against me was hearsay and stories from people I can't guarantee even like me. Being that everyone in that store was interviewed about the subject, I felt my character and reputation were sabatoged, that everyone knew about it, and I couldn't bear to even show my face. I stuck it out as long as I could, to see where the investigation went, they finally offered me the option of demotion, or transferring to an even more dangerous store, but they said if I chose to stay at my store and had any contact with that employee, or even crossed backline to say hey, I would be automatically terminated, now in my defense, that is damn near impossible in my line of work. I felt sabatoged.