21 lines
2.3 KiB
TeX
21 lines
2.3 KiB
TeX
We thus showed that the specific geometry of the intersecting D-branes leads to different results when computing the value of the classical action, that is the leading contribution to the Yukawa couplings in string theory.
|
|
In particular in the Abelian case the value of the action is exactly the area formed by the intersecting D-branes in the $\R^2$ plane, that is the string worldsheet is completely contained in the polygon on the plane.
|
|
The difference between the \SO{4} case and \SU{2} is more subtle as in the latter there are complex coordinates in $\R^4$ for which the classical string solution is holomorphic in the upper half plane.
|
|
In the generic case presented so far this is in general no longer true.
|
|
The reason can probably be traced back to supersymmetry, even though we only dealt with the bosonic string.
|
|
In fact when considering \SU{2} rotated D-branes part of the spacetime supersymmetry is preserved, while this is not the case for \SO{4} rotations.
|
|
|
|
In the general case there does not seem to be any possible way of computing the action~\eqref{eq:action_with_imaginary_part} in term of the global data.
|
|
Most probably the value of the action is larger than in the holomorphic case since the string is no longer confined to a plane.
|
|
Given the nature of the rotation its worldsheet has to bend in order to be attached to the D-brane as pictorially shown in~\Cref{fig:brane3d} in the case of a $3$-dimensional space.
|
|
The general case we considered then differs from the known factorised case by an additional contribution in the on-shell action which can be intuitively understood as a small ``bump'' of the string worldsheet in proximity of the boundary.
|
|
|
|
In a technical and direct way we also showed the computation of amplitudes involving an arbitrary number of Abelian spin and matter fields.
|
|
The approach we introduced does not generally rely on \cft techniques and can be seen as an alternative to bosonization and old methods based on the Reggeon vertex.
|
|
Starting from this work the future direction may involve the generalisation to non Abelian spin fields and the application to twist fields.
|
|
In this sense this approach might be the only way to compute the amplitudes involving these complicated scenarios.
|
|
This analytical approach may also shed some light on the non existence of a technique similar to bosonisation for twist fields.
|
|
|
|
|
|
% vim: ft=tex
|