Green functions and twist correlators for N branes at angles

We compute the Green functions and correlator functions for N twist fields for branes at angles on T2 and we show that there are N−2 different configurations labeled by an integer M which is roughly associated with the number of reflex angles of the configuration. In order to perform this computation we use an SL(2,R) invariant formulation and geometric constraints instead of Pochammer contours. In particular the M=1 or M=N−1 amplitude can be expressed without using transcendental functions. We determine the amplitudes normalization from N→N−1 reduction without using the factorization into the untwisted sector. Both the amplitudes normalization and the OPE of two twist fields are unique (up to one constant) when the ϵ↔1−ϵ symmetry is imposed. For consistency we find also an infinite number of relations among Lauricella hypergeometric functions.