  We develop a diagrammatic language for symmetric product orbifolds of
two-dimensional conformal field theories. Correlation functions of twist
operators are written as sums of diagrams: each diagram corresponds to a
branched covering map from a surface where the fields are single-valued to the
base sphere where twist operators are inserted. This diagrammatic language
facilitates the study of the large N limit and makes more transparent the
analogy between symmetric product orbifolds and free non-abelian gauge
theories. We give a general algorithm to calculate the leading large N
contribution to four-point correlators of twist fields.
