MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I would like clarification of 26 dimensional Bosonic String Theory. A definition would be, that this is free bosons compactified on a torus and orbifolded by a 2-point reflection group (or asymmetrical Z2 grading), induced by the Leech Lattice.

  1. Is this "asymmetrical" because of the 25,1 signature, where Z2 contributes to 1 space and 1 time dimension
  2. Is this the Lorentzian form, which adds 2 dimensions of the worldsheet, 24 + 2, and how is this related to a vertex operator algebra, with Z2 grading, which I still don't understand, how VOAs work in the context of the Monster group (which is the symmetries of the vertex operator algebra of this structure, on an even II(25,1) lattice). I understand about the Leech Lattice, tori, orbifolding, etc. but everything together, is a bit overwhelming to understand.

I may have some terms wrong, but I still haven't found a one paragraph explanation of how all this works, and how it relates to the Monster, Moonshine, VOAs, CFTs, etc. I do know that VOA's are to the Leech Lattice as the Lattice is to the Golay Code (and M24), and that this is analogous to E8 lattice being based on the Hamming code, and in turn, the E8 group being based on the E8 lattice, in similar fashion. Is the above an attempt to create an infinite dimensional structure (The Fake Monster Lie Algebra) with the Simple Monster group which somehow parallels what is going on with E8 and Lie Algebras?

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.