Natural Science Forum / Physics / Research / September 2007

Classical superstrings exist in dimensions D=3,4,6,10 reflecting the
triality construction, that happens to be valid for say k=1,2,4,8 via
division algebra stuff and all that. This is well known, specially
from the work in the Brane Scan but also older papers by Evans and by
Sierra.

Now, I wonder: Does the triality stuff reflects in the purely bosonic
strings? On one side it can be said that classical bosonic strings
exist for any dimension. On other hand, there are two ways to see the
D=26 coming from D=10.

a) by Bott peridicity, because Cl(25,1) comes to be similar to
Cl(9,1).
b) by tripling: (10-2)*3=(26-2)

In the case a, the dimension D=26 should be seen coming from k=8 via
16+(k+2). In the case b it would be be (3*k)+2. So we could have two
families of special bosonic string theories.

perhaps
a)  for D= 19, 20, 22, 26
or perhaps
b)  for D= 5, 14, 20, 26

has anybody seen such beasties?

A related question is why quantization isolates D=10 and D=26. In some
presentations quantization seems a requisite completely different from
triality, but in the GS superstring formulation it is used to build
space-time susy.

Alejandro
PS: Just if you are wondering, I still do not believe in string
theory. But I am a bit intrigued about some features.
Alejandro