"Aaron Bergman" <aberg...@physics.utexas.edu> schrieb im Newsbeitrag
> In articleLet me try to make this more precise, using the stuff from hep-th/0409200:
> Urs Schreiber <Urs.Schrei...@uni-essen.de> wrote:
>> On Mon, 3 Jan 2005, Aaron Bergman wrote:
>> > In article <33soqpF43pvupU1-100...@individual.net>, Urs Schreiber
>> > > The gauge field on the D-brane is not part of this data but enters
>> > No. They're linked.
>> Yes, they are linked, but the 1-form on the D-brane is not the 1-form in
> I'll have to read your paper. When I read JB's paper back when, I
An F-string on a stack of D-branes in the presence of a Kalb-Ramond field is
[G_Q] = [lambda_ijk, alpha_ij, beta_i]_Q ,
fulfills the relation
[G_Q] = [1,0,B_Q] + [D(G_ij, A_i)] + [omega_ijk,0,0] .
On the left is the Deligne class of the abelian 1-gerbe, on the right is
[1,0,B_Q] - the abelian gerbe coming from the Kalb-Ramond field B
[D(G_ij,A_i)] - the abelian lifting gerbe of the (possibly twisted)
[omega_ijk,0,0] - something related to spinors that I am going to ignore in
This is how the gerbe, the Kalb-Ramond field and the D-brane gauge field A
alpha_ij = G_ij(d+A_j)G_ij^-1 - A_i
i.e., they measure the twist in the connection on the branes.
As Aschieri and Jurco emphasize in their paper, the form of the right hand
This is of importance for the step to one dimension higher.
A (twisted) nonabelian bundle can be called a (twisted) nonabelian 0-gerbe.
- an abelian p-gerbe coupled to the bulk
- a (twisted) nonabelian (p-1)-gerbe coupled to the boundary
of the p-"brane", for p=1.
Going up one dimension the above scenario becomes concerned with a membrane
The holonomy of the abelian 3-form C on a 3-cycle is computed by abelian
By a reasoning completly analogous to that above, [CS] can be written as
[CS] = [D G] + [1,0,0,C] + [theta_ijkl,0,0,0].
Here D is again the nonabelian Deligne operator and G now denotes a possibly
By comparison with the above, the nonabelian gerbe G with cocylce data G =
This 2-form is not the Kalb-Ramond 2-form but the nonabelian generalization
Similarly, the A_i enetering the nonabelian gerbe cocycle here are not in
So once one understands holonomy of nonabelian 2-gerbes one should get that
a 2-brane ending on a stack of branes is described by
- an abelian 2-gerbe coupled to the bulk
- a (twisted) nonabelian (2-1 = 1)-gerbe coupled to the boundary
of the 2-brane,
just as above for 1-dimension lower.
The closest relation of the nonabelian 1-gerbe cocylce data to a D-brane
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