Question

Are these 2D conformal field theories the same or related?

Answer 1

Consider the following 2D conformal field theories:

26D bosonic string theory compactified on the Λ24Λ24 Leech lattice torus.
10D N=1 Superstring Theory (any of the 5 as they are all dual) compactified on the E8E8 lattice torus.
N=(2,0) superconformal 6D theory compactified on the F4F4 lattice torus.
N=4 Super Yang Mills Theory (for some gauge group SU(n)) on the G2G2 (hexagonal lattice) torus.
N=8 Superconformal Chern-Simons Theory in 3D compactified on a line segment.
i.e. Taking (possibly) the most symmetric field theory in these dimensions and compactifying it on a lattice torus which is the most densest lattice (from sphere packing) which is 2 dimensions less.

They all produce a 2D (conformal?) field theory. The first one gives the Monster Conformal Field Theory. Now, it seems that because of there is so much constraints that these other theories should either produce the same Monster CFT or another CFT related to an interesting group?

What is more, if they all can be compactified to the same (or related) 2D conformal field theories, does this imply dualities between all these theories?

To me it seems there is this hierarchy of theories related to densest sphere packings. Which could be related to a hierarchy of groups with the Monster at the top. That's what it looks like but is there any truth in this?

I believe the first case it's call Monstrous Moonshine.

(BTW. I Think this is really a math question but I would guess it is more relevant to theoretical physics).

Note also that all these theories obey the equation (D−2)×N=8(D−2)×N=8. If we set for 26D bosonic theory N=13N=13. (But it doesn't really have any supersymmetry).

Answer 2

they are same. hope it help you