Worldsheet Derivation of a Large N Duality

TL;DR

This paper provides a worldsheet proof of the duality between U(N) Chern-Simons theory on S^3 and topological strings on the resolved conifold, revealing a new branch that introduces open string sectors and explains the `t Hooft expansion.

Contribution

It introduces a worldsheet perspective on the duality, showing how open string sectors emerge from a new branch of the worldsheet and clarifying the relation to gauge theory amplitudes.

Findings

Identification of a new branch in the worldsheet corresponding to open strings.

Reproduction of `t Hooft expansion through worldsheet fluctuations.

Discovery of additional terms in closed string amplitudes beyond `t Hooft expansion.

Abstract

We give a worldsheet proof of the equivalence between the U(N) Chern-Simons gauge theory on S^3 and the topological closed string theory on the resolved conifold geometry. When the `t Hooft coupling of the gauge theory is small, the dual closed string worldsheet develops a new branch. We show that the fluctuations of the worldsheet into this branch effectively correspond to ``holes'' on the worldsheet, generating an open string sector. This leads to a microscopic description of how the `t Hooft expansion of gauge theory amplitudes is reproduced in the closed string computation. We find that the closed string amplitudes also contain terms which are not captured in the `t Hooft expansion but are present in the exact computation in the gauge theory amplitudes. These arise when the whole Riemann surface is in the new branch. We also discuss the cases with SO and Sp gauge groups.