There’s a list available in the PS4 Web Content Guidelines.
Strange thing though: Which browsers and operating systems support Let’s Encrypt says the PS3 is supported, but the root certificate list for PS3’s is even shorter, without IdenTrust’s DST Root X3-thingy : http://us.playstation.com/pscomauth/groups/public/documents/webasset/ps_web_content-guidelines_2.70.pdf
So how is that possible?