String Group from 2-Groups

[Urs Schreiber]

We have a new preprint

J. Baez, A. Crans, U. Schreiber & D. Stevenson

From Loop Groups to 2-Groups,

math.QA/0504123
http://golem.ph.utexas.edu/string/archives/000547.html .

It proves the following two theorems:

1) The weak Lie 2-algebras g_k defined in HDA6 are equivalent to
infinite-dimensional strict Fréchet Lie 2-algebras P_k g. These are related
to the Kac-Moody central extension ?_k g of the loop algebra ? g and come
from infinite-dimensional Fréchet Lie 2-groups Omega_k G.

2) The nerve |P_k G| of P_k G is, for G=Spin(n), the topological group
String(n).

Hence 2-bundles and gerbes with structure 2-group P_k G should be related to
"String(n)-bundles" and 2-connections on them possibly to the enriched
elliptic objects defined by Stolz and Teichner.

[Thomas Larsson]

Post by Urs Schreiber
We have a new preprint
J. Baez, A. Crans, U. Schreiber & D. Stevenson

From Loop Groups to 2-Groups,

math.QA/0504123
http://golem.ph.utexas.edu/string/archives/000547.html .

From a plaquette-gluing point of view, a surface holonomy is equipped
with a string of indices, one for each link on the boundary; I call this
a "barbed wire". Hence there is an independent gauge transformation for
each point on the boundary loops, so the global gauge group must be a
loop group rather than a finite-dimensional group. It is interesting that
you are also led to loop groups, from your quite different starting point.
Maybe our opinions on what a 2-gauge theory is will one day converge.

But you are still stuck with abelian 3-curvature, arent you? This seems
difficult to reconcile with a generic non-abelian gauge theory in loop
space, if that if what we want.

[nightcleaner]

In another thread there is a question about strings vibrating in five
dimensions. These dimensions are said to be spatial. Is there a
formula that the uninitiated might look at and be able to see where the
idea of five dimensions fits in? And is there any indication I could
recognise about if these five dimensions include the usual three
spatial dimensions of geometry? Am I to assume that two of them then
are collapsed, perhaps Calabi-Yau type dimensions? Or could one of
more of them be large?

Thanks

Richard Harbaugh

[Moderator's note: Probably April 2005, update. LM]