I try to understand what the Monster CFT and its possible connection to 3 dimensional gravity at ($c=24$) is about (see https://arxiv.org/abs/0706.3359)

To my best understanding (and please correct me if here are anywhere wrong statements) the Monster CFT has an extended (with respect to the Virasoro algebra) chiral algebra.

- Do the elements of the extended chiral algebra, other than the Virasoro algebra, also create new states (like e.g., models with affine Kac-Moody algebras)?

The Virasoro primary fields fall into irreducible representations of the Monster.

- How many irreducible representations are there? Are there finitely many of them?

At least according to http://www.ams.org/notices/200209/what-is.pdf there are 194 complex irreducible representations.

If I understand this correctly, then the coefficients of the $J$ invariant (see https://en.wikipedia.org/wiki/Monstrous_moonshine , $r_n$ is the dimension of the irreducible representation $r_n$)

$J(q)=r_1 q^{-1}+ (r_1+r_2) q+ (r_1+ r_2+r_3) q^2+ ...$

should get at some point no new contributions from new representations, i.e., there should be no term $r_{195}$.

- Did I understand this correctly?

If that is correct then I'm puzzled by the following: The dimension $r_n$ means that there are $r_n$ new Virasoro primary fields at that this level. These in turn should "correspond" to black holes (https://arxiv.org/abs/0706.3359).

- If 3. is correct, why should there be no new Virasoro primaries after some level. What happens to the black holes at this level?

This post imported from StackExchange Physics at 2017-08-26 13:34 (UTC), posted by SE-user ungerade