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We consider the classical instantonic contribution to the open stringconfiguration associated with three D-branes with relative rotation matrices inSO(4) which corresponds to the computation of the classical part of thecorrelator of three non Abelian twist fields. We write the classical solutionas a sum of a product of two hypergeometric functions. Differently from all theprevious cases with three D-branes, the solution is not holomorphic andsuggests that the classical bosonic string knows when the configuration may besupersymmetric. We show how this configuration reduces to the standard Abeliantwist field computation. From the phenomenological point of view, the Yukawacouplings between chiral matter at the intersection in this configuration aremore suppressed with respect to the factorized case in the literature.

The Classical Solution for the Bosonic String in the Presence of Three D-branes Rotated by Arbitrary SO(4) Elements