Disqus makes a request vio OAuth to authenticate you via Facebook. It then stores the authentication token which will authenticate you to Facebook in the future

Disqus makes a request vio OAuth to authenticate you via Facebook. It then stores the authentication token which will authenticate you to Facebook in the future until you revoke it. Also by putting the Disqus javascript widget on your page you will probably have cookies for: example.com disqus.com and example.disqus.com (if example was your disqus site name).