Green functions and twist correlators for $N$ branes at angles

TL;DR

This paper calculates Green functions and correlators for N twist fields on T^2 with branes at angles, revealing N-2 configurations and deriving explicit formulas using geometric methods, with implications for string theory amplitudes.

Contribution

It introduces a geometric approach to compute twist field correlators for branes at angles, avoiding transcendental functions and establishing normalization and OPE properties.

Findings

Identifies N-2 distinct configurations labeled by M.

Provides explicit formulas for M=1 and M=N-1 amplitudes.

Establishes normalization and OPE uniqueness under symmetry constraints.

Abstract

We compute the Green functions and correlator functions for N twist fields for branes at angles on T^2 and we show that there are N-2 different configurations labeled by an integer M which is roughly associated with the number of obtuse angles of the configuration. In order to perform this computation we use a 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 \epsilon <-> 1-\epsilon symmetry is imposed. For consistency we find also an infinite number of relations among Lauricella hypergeometric functions.