DualN- Point Functions inPGL(N−2,C)- Invariant Formalism

Abstract

We derive a new expression for the dual $N$ -point function integrand which is invariant under the action of the projective general linear group $\mathrm{PGL}(N\ensuremath{-}2,C)$. The $(N\ensuremath{-}1)(N\ensuremath{-}3)$ free complex parameters of the group are used to make the integrand independent of the values of ($N\ensuremath{-}1$) points of complex dimension ($N\ensuremath{-}3$) which appear in the integrand. These points uniquely specify the location of all $\frac{1}{2}(N\ensuremath{-}1)(N\ensuremath{-}2)$ hyperplanes which appear as branch singularities of the integrand when it is viewed as a function on ($N\ensuremath{-}3$) -dimensional complex projective space. In contrast to the Koba-Nielsen formalism, the $\mathrm{PGL}(N\ensuremath{-}2,C)$ -invariant form of the $N$-point integrand allows transformations which mix the ($N\ensuremath{-}3$) integration variables and permits greater freedom in the placement of the branch singularities while preserving a simple hyperplane structure for the singularities.