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$T^2$ and we show that there are N−2$N-2$ 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)$\mathit{SL}(2,\mathbb{R})$ invariant formulation and geometric constraints instead of Pochammer contours. In particular the M=1$M=1$ or M=N−1$M=N-1$ amplitude can be expressed without using transcendental functions. We determine the amplitudes normalization from N→N−1$N\to N-1$ 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 ?↔1−?$?\leftrightarrow 1-?$ symmetry is imposed. For consistency we find also an infinite number of relations among Lauricella hypergeometric functions.