As carrots ferment the brine might at some point become a little slimy and thick. Don't worry yet. This stage will usually pass and the brine will return to its watery self. This is caused by butyric acid-producing bacteria(clostridium) that takes hold early on when the lactobacillus hasn't populated the ferment yet. Usually, the lactobacillus will overtake and the ferment will be good when done. It usually happens at higher temperatures and with vegetables like carrots, beets and radishes. Usually but not always the brine will normalise if all goes well and the lactobacillus wins the race in souring the brine. If the ferment does not sour after about 4/5 days. Discard the batch as bad bacteria won the race. If it's still slimy after 28 days, throw it out. Wild fermentation comes with the risk of bad bacteria spoiling a batch. Rare but it happens. So, rather be safe and start over. To prevent this from ever happening in the first place, simply add a cup or so of starter culture in the form of brine from another ferment like fermented cucumbers or sauerkraut.