Worldsheet derivation of a large N duality Original Research Article

We give a worldsheet proof of the equivalence between the U(N) Chern–Simons gauge theory on S3 and the topological closed string theory on the resolved conifold geometry. When the ʹt 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 ʹt 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 ʹt 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.