# If QFT is a sum over 1-D topologies and String Theory over 2-D topologies, what is the corresponding theory for N-D topologies?

My understanding is that perturbative QFT can essentially be described as a weighted sum over 1-D topologies (ie Feynman graphs), and String theory is essentially the generalization to a sum over 2-D topologies. Why do we stop here? Is there a name for the theory defined as the sum over 3-D, or N-D topologies?

• Essentially a duplicate of physics.stackexchange.com/q/55431/2451 , physics.stackexchange.com/q/66948/2451 and links therein. Jun 13 '14 at 16:54
• Ah, thanks, I hadn't found those before. They do basically ask the same question, although I would complain that their answers are too technical (if I was a string theorist I would know the answer already!) Jun 13 '14 at 17:03

While it originally began as a theory of 1-dimensional strings, today it describe a quantum theory of many other $p$-dimensional (D$p$-branes, membranes, etc.). We just didn't bother finding another name for the theory. The key difference is that while a fundamental string is perturbative, the other objects are not (since they are very heavy)