Welcome to MathOverflow

Question

14

2

I am doing a project on the inverse Galois problem, and am seeking to show that the monster group is realisable over the rationals. I have heard that the monster group has found uses in theoretical physics, and was wondering what those uses might be. Also, is there any practical significance to theoretical physics in the result I am aiming to prove?

flag	asked Mar 20 2011 at 18:56 Amin Saied 141●3

2

Take a look at mathoverflow.net/questions/13851/… for information on realizing the Monster group as a Galois group over Q. No mention there of applications to physics, so this is not a direct answer to the question. – KConrad Mar 20 2011 at 19:52

3

There is a book called "Moonshine Beyond the Monster: the bridge connecting Algebra, Modular Forms and Physics" which was written by Terry Gannon. I think it's probably a good idea for you to take a look at it ;). – Max Muller Mar 21 2011 at 8:11

Richard Borcherds · Answer 1 · 2011-03-21 04:26:25Z UTC

There are presently no applications of the monster group in physics, though there is a lot of misleading speculation about this. However in the other direction there are some applications of ideas from physics to the monster group. In particular the no-ghost theorem in string theory is used to construct the monster Lie algebra acted on by the monster group.

The ideas from physics seem to have no direct connection with the problem of realizing the monster as a Galois group over the rationals. This was solved by Thompson, who showed by character-table calculations that the monster satisfies a sufficient condition ("rigidity") for it to be a Galois group.

Mohamed Alaa El Behairy · Answer 2 · 2011-06-09 22:49:29Z UTC

0

I know very little about the subject; But you can check this lecture : cosmolearning.com/courses/… by Ed Witten where he links the Monster group to quantizing gravity in 2+1 dimensions. In particular, the lecture contains a very interesting derivation of black hole entropy in 2+1 as log(196883)=12.19.. , where the classical entropy is 4∗π=12.57 which is off by a few percent. What do you think of that professor Borcherds?

answered Jun 9 2011 at 22:49

Mohamed Alaa El Behairy
124●1●5

2

Witten's work in this area is well-known, and he has written a preprint that was widely read: arxiv.org/abs/0706.3359 This does not seem to be an application of the monster group in physics, but it indicates the potential for a relationship to exist. – S. Carnahan♦ Jun 10 2011 at 4:54

Thanks for the suggestion; But can you elaborate more why this does not seem to be an application of the monster group in physics ? – Mohamed Alaa El Behairy Jun 10 2011 at 5:32

Witten doesn't use the monster group anywhere in his paper. He describes a conjectural correspondence between pure 3d gravity in $AdS_3$ space and extremal conformal field theories. In the case of central charge 24, the only known extremal CFT has monster symmetry, but the uniqueness of the moonshine module as an extremal CFT with that central charge is still conjectural, and that symmetry does not seem to appear naturally on the gravity side. In particular, the entropy calculation uses a 196883 dimensional vector space, but does not use a monster action on it. – S. Carnahan♦ Jun 11 2011 at 13:58

The Monster Group uses in mathematical physics

Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)

2 Answers

You can accept an answer to one of your own questions by clicking the check mark next to it. This awards 15 reputation points to the person who answered and 2 reputation points to you.