On the geometry of classically integrable two-dimensional non-linear sigma models

Abstract

A master equation expressing the classical integrability of two-dimensional non-linear sigma models is found. The geometrical properties of this equation are outlined. In particular, a closer connection between integrability and T-duality transformations is emphasised. Finally, a whole new class of integrable non-linear sigma models is found and all their corresponding Lax pairs depend on a spectral parameter.

16 pages. Major changes (almost a new paper). To be published in Nuclear Physics B (2010)

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