The Quantum Structure of Space and Time (293 pages)

162 The Quantum Structure of Space and Time

how good any classical limit is and which classical limit applies in any given

computation. That would be useful for many people.

P. Ramond I do not know about being useful. First a remark about landscape.

I just saw in a museum of ancient art Hieronymous Bosch’s temptation of Saint

Anthony, let me not say more.

The second thing is about some no-go theorems that we should be aware of.

There are no-go theorems about massless particles of spin higher than two. If

they are taken one at a time, there is no doubt that the no go-theorems apply.

If there are an infinite amount, it is an open question. Moreover, there are

mathematical structures based on the coset F4/SO(9), which is of great mathe-

matical interest actually, that basically contain the fields of N = 1 supergravity

in eleven dimension as its lowest level. One should not think this is completely

about things that are known. This presents great difficulties, but one should

keep an open mind and try to look at these things without giving up.

J. Harvey I think of the areas of mathematics that have been discussed here,

the one that to me seems to have some of the strongest hints, but the least

understood, is the general question of Elo, Borcherds algebras, generalized Kac-

Moody algebras. In Nicolai’s talk, to the degree I understood it, there definitely

seems to be some structure going on, where El0 is reflected in eleven dimensional

supergravity. But when he was talking about higher level in the landscape of

these representations, I think it was about one in a billion that actually fit into

the structure that we know so far, and we don’t know what the rest of these are

doing. In calculations I did with Greg Moore number of years ago, we found

denominator formulas for Borcherds algebras coming out of definite one-loop

string integrals. We tried to give an algebraic explanation of this but we failed.

I do not think that these things can be coincidences. I think there is a very

general algebraic structure which will allow us to have much greater control

over some supersymmetric theories. I do not think it will solve the real world

problem of what we do without supersymmetry or time evolution. But it seems

to me to be an example of not drilling where the board is thinnest, but where

it is thin enough that we might actually get through it.

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