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Integrability and String Theory

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The problem of free string motion in curved spacetime is relevant for understanding the large-N limit of SU(N) gauge theory. In some of the most interesting cases, the spacetime is a symmetric space and string motion is exactly integrable due to an old result of Eichenherr and Forger. In other words it exhibits an infinite tower of Poisson-commuting conserved quantities. I will review the role of classical and quantum integrability in recent progress towards an exact solution for the string spectrum in these backgrounds.

This talk is part of the CMS Colloquia series.

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