carrots wilted

If they weren't protected against carrot fly it's odds on that's what's happened, although the first sign is usually the foliage turning a pinky-red colour.

If you mean it's the edge of the carrot patch rather than the edge of all the leaves I suppose it's possible they've caught some weedkiller spray drift (look for evidence of other plants dying.)

Pull one up and look at the roots. Carrot fly maggots or some other bug has probably knipped off the taproot. This may have been done for some time but is only showing now there has not been rain for a few days.

Pull up and examine the roots of one of the affected plants as Salmo suggested - growing carrots 2-3' above the surrounding soil level improves the chances of avoiding carrot fly but doesn't come with a guarantee.