I wasn't aware of the link between string nets and spin networks until Buerschaper et al (string net -> tensor network) and Singh et al (tensor network -> spin network). Is there a more direct connection?
Also, what is the relationship between AdS/CFT and tensor networks? I remember reading a Horowitz and Polchinksi review that said AdS/CFT is an example of emergent gauge theory, which cited D'Adda 1978 - whom Levin and Wen also cite, so was a little aware that AdS/CFT and string nets had a common descent - but haven't any understanding beyond that.
Edit: Wow, I just saw you actually work on this stuff, unlike people like me who just read about it - very cool!