Worldsheet Derivation of a Large N Duality

Details Worldsheet Derivation of a Large N Duality Worldsheet Derivation of a Large N Duality

2002-05-29

arxiv.org/abs/hep-th/0205297v3

Nucl.Phys.B641:3-34,2002

Physics

High Energy Physics

High Energy Physics - Theory

39 pages, 9 figures

Scientific paper

10.1016/S0550-3213(02)00620-X

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.

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