Yes it seems that it is possible. See for example arXiv:cond-mat/0411752 where some models are constructed, but I (naively) think one can readily generalize the whole logic of Levin-Wen models to any dimension and any types of branes (the mathematical input might then be something more exotic than tensor categories?). But I think that excitations of these models will generically be extended objects, for example the boundaries of open membranes will be string-like object. One could also imagine that low-energy effective theories if these models might not be conventional (topological) field theories, but string- and brane-field theories (this is however not the case in the above reference it seems).

I don't know enough about this to say much more, but I know others on this site know a lot more. I hope they will give their take on this question.

This post imported from StackExchange Physics at 2014-04-05 16:22 (UCT), posted by SE-user Heidar