Where we live we have a bad problem with ants. What they do in the garden when they are in large enough numbers is destroy some of the plants. Last year we lost 30 of our 48 Jalapenos to the ants. What they do in our garden is tunnel next to the root systems and then the roots seem to dry and the plants begin to wilt. Basically they destroy the root system of the plants.
The only way of controlling them has been to put powder Seven in the hole when we plant. This has happened over that last four or five years. But this year we seem to be doing better with all our plants only losing one pepper and one tomato to the ants.
Our soil is heavy toward being sandy and it makes a great place for the ants to make the whole yard an ant hill.
Try some diatomaceous earth. Any insects crawling over it find it cuts their "skin". I always run for than when I see the first sign of ants moving in. It is non toxic but one should use a face mask or make sure you don't breath in the fine powder. It would be safe around your peppers.
My garden is lined with really old railroad ties, and little black ants like to nest in the rotten wood. Unfortunately, they also like my veggies - especially okra. Okra has sap they like, and they get around the base of the pods and eventually ruin them.
I don't get carried away about controlling ants, but when I see about a million of them on a railroad tie about to swarm, Ortho Bug-B-Gone takes care of them real quick. I figure people who are a lot more qualified than me have approved the use of such products by home gardeners.
One thing to really watch for with ants is APHIDS. The ants will farm the aphids to get the honeydew they secrete. They will defend the aphids against predators and can cause aphid populations to get out of control. It's definitely something to watch for. I had a bad problem early in the season here in Texas. I had to resort to Captain Jack's Dead Bug Brew (spinosad) and that really got things under control fast. It will kill the beneficial insects, too, including bees, so be careful with that. Good luck!
I have noticed that ants know when a melon is ripe. They will collect at the area where stem meets fruit. I've not noticed this in prior years and am wondering if it is because it has been so dry this year.