Diagrams for Symmetric Product Orbifolds

TL;DR

This paper introduces a diagrammatic approach to compute correlation functions in symmetric product orbifolds of 2D conformal field theories, simplifying large N analysis and highlighting gauge theory analogies.

Contribution

It develops a novel diagrammatic language for symmetric product orbifolds, enabling systematic calculation of correlation functions and large N behavior.

Findings

Diagrammatic representation of twist operator correlators.

Algorithm for leading large N four-point functions.

Enhanced understanding of gauge theory analogies.

Abstract

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.