Abstract
We consider the simplest possible setting of non-abelian twist fields which corresponds to SU(2) monodromies. We first review the theory of hypergeometric function and of the solutions of the most general Fuchsian second order equation with three singularities. Then we solve the problem of writing the general solution with prescribed U(2) monodromies. We use this result to compute the classical string solution corresponding to three D2 branes in R4. Despite the fact that the configuration is supersymmetric the classical string solution is not holomorphic. Using the equation of motion and not the KLT approach we give a very simple expression for the classical action of the string. We find that the classical action is not proportional to the area of the triangle determined by the branes intersection points since the solution is not holomorphic. Phenomenologically this means that the Yukawa couplings for these supersymmetric configurations on non-factorized tori are suppressed with respect to the factorized case.
Highlights
Introduction and conclusionsSince the beginning, D-branes have been very important in the formal development of string theory as well as in attempts to apply string theory to particle phenomenology and cosmology
Some of the previous results were obtained in the infinite charge formalism and boundary state formalism [7]
In [10] and [11] based on previous results [12] and a mixture of the path integral approach with the Reggeon approach the generating function of all the correlators with an arbitrary number of twist fields and usual vertices was given in the case of abelian twist fields
Summary
D-branes have been very important in the formal development of string theory as well as in attempts to apply string theory to particle phenomenology and cosmology. In [10] and [11] based on previous results [12] and a mixture of the path integral approach with the Reggeon approach the generating function of all the correlators with an arbitrary number of (excited) twist fields and usual vertices was given in the case of abelian twist fields. These computations boil down to the knowledge of the Green function in presence of twist fields and of the correlators of the plain twist fields. We clearly show that in the holomorphic case the action has a geometrical meaning
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