Towards a fully stringy computation of Yukawa couplings on non factorized tori and non abelian twist correlators (I): the classical solution and action

Understand

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 $R^4$.