Nonperturbative Quantum Theories and Integrable Equations

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Abstract
I review the appearance of classical integrable systems as an effective tool for the description of nonperturbative exact results in quantum string and gauge theories. Various aspects of this relation: spectral curves, action-angle variables, Whitham deformations and associativity equations are considered separately demonstrating hidden parallels between topological 2d string theories and naively nontopological 4d theories. The proofs are supplemented by explicit illustrative examples.
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