According to the paper ``Heterotic and Type I String Dynamics from Eleven Dimensions'' (page 7):

Even when the topology is wrong -- for instance on $\mathbb{R}^{11}$ where there is no two-cycle for the membrane to wrap around -- macroscopic membrane solutions (with a scale much bigger than the Planck scale) will make sense, but we do not assume they can be quantized to recover gravitons.

This seems like a result from basic topology that I ought to know. But in general, how do I know whether there is a $k$-cycle for a membrane to wrap around a given manifold $\mathcal{M}$?

In this particular case, is it just that $\mathbb{R}^{11}$ has genus 0, and hence not even a one cycle to wrap around?

Possibly related thread which does not answer my question: What does it mean to "wrap" a D-brane around some manifold?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.