[bvv]

It's a little complicated. The idea is that one uses this Leech lattice to define a 24-dimensional space, and we throw in little quantum strings that live on that space. These strings are inspired by (but not exactly the same as) the strings we know from standard 'string theory'.

The quantum field theory is then the one living on the worldsheet of the strings, it is the one that describes their embedding in this peculiar space. The monster group turns out to be a symmetry group of this field theory.

This is all conjecturally related to quantum gravity (according to Witten's paper) through the so-called AdS/CFT correspondence which states that field theories are sometimes equivalent to theories of quantum gravity. It has its problems and it remains to be seen if it is really true. (AdS/CFT is fine in itself, the trouble of the conjecture is whether it holds in this particular example.)

A word of warning based on previous experience: this is highly technical stuff and what is mentioned here are just words. Please don't think you can make contributions to this field without seriously studying the equations.