When can I let my child go down a slide without me?

Depends... ...On how long, how steep and how protected the slide is, and what the child is sliding into.
Depends. This depends a lot on your child's development. In order to safely go down a slide on her own, a child has to be walking well, and also has to understand that she is supposed to stay seated the whole time while on the slide, and has to understand how to land on her feet at the bottom. If she can't do any of these three things, she's not ready to be on the slide by herself.