The photosymbionts are cyanophytes (= cyanobacteria): Prochloron in many host species and Synecocystis in some other species.
Prochloron is a very unique cyanophyte, because it has chlorophyl a and b and lacks phycobilin.
Trididemnum clinides harbors three cyanophyte species in the tunic (see Hirose, Uchida & Murakami, European Journal of Phycology, 2009).
Interestingly, non-Prochloron cyanophytes are only found in the tunic.
Prochloron