In basic string theory Lagrangians (e.g. the Polyakov or the Nambu-Goto), the variables include a function $x:X\rightarrow M$ embedding a world-sheet $X$ into some target space $M$, which can be Minkowski space or some curved target space. Is it possible to reformulate these theories to eliminate the target space? Perhaps to replace it with sections of some bundle over $X$? Although this would seem to amount to just some kind of $(1+1)$-dimensional quantum field theory?
I realize this is a somewhat open-ended question; I'm just wondering if there has been any research done toward formulating string theories that might not involve any dependence on a target space.