Rude Co-Worker

It was brought to my attention that a co-worker I have absolutely hates my guts. I assume it's jealousy as I got the role they wanted. especially since I did not apply for the role, I simply showed up to work to find I had been promoted. I found out that they have been bad mouthing me ever since I got it which has been about a year and a half now. I have almost never interacted with this person as they work a different shift than I do. I knew they never liked me which is fine, HOWEVER, I just learned they've been absolutely trashing my name. They've been telling others that I am illiterate, deserve to be fired, a complete idiot. What's worse is the shift there on the two supervisors AND manager have 100% heard this from them and have taken no action on their toxicity. Where I work we have a zero tolerance policy for this. So I come to find out that my name is being dragged through the mud and management is turning a blind eye. It hurts. I have been trying my best and it hurts.