A/C suddenly stopped working?

I found a burned hole through the wire that connects under the engine cover. The wire runs from the compressor to the engine harness I'm assuming. The hole is on the engine side of the connector. Can you tell me what this part is called? I'm looking at and seeing an A/C compressor pigtail. I hope this is the part. Could you also tell me how to connect the loose wires if this is the right part. Thank you so much.