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Rajesh Gopakumar : exp(N) (Feb 3, 2000 4:00 PM)

The connection between large N gauge theories and string theories is typically made perturbatively. Namely, the Taylor expansion in 1/N corresponds to the genus expansion in string theory. Instanton effects in the gauge theory, however, go like exp(-N) and correspond to non-perturbative effects in the string theory. I will argue, in the context of the N=4 super Yang-Mills theory, how very non-trivial large N non-renormalization theorems in this instanton sector follow simply from the dual string description. The argument assumes little other than the existence of a derivative expansion in string theory. As a particular example, one can explain the striking agreement found by Dorey et al between certain weak coupling instanton calculations and the strong coupling predictions of supergravity.

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