Multi-trace correlators from permutations as moduli space

A bstract We study the n -point functions of scalar multi-trace operators in the U( N c ) gauge theory with adjacent scalars, such as N = 4 super Yang-Mills, at tree-level by using finite group methods. We derive a set of formulae of the general n -point functions, valid for general n and to all orders of 1/ N c . In one formula, the sum over Feynman graphs becomes a topological partition function on Σ 0, n with a discrete gauge group, which resembles closed string interactions. In another formula, a new skeleton reduction of Feynman graphs generates connected ribbon graphs, which resembles open string interaction. We define the moduli space ℳ g , n gauge from the space of skeleton-reduced graphs in the connected n -point function of gauge theory. This moduli space is a proper subset of ℳ g , n stratified by the genus, and its top component gives a simple triangulation of Σ g , n .