Integrable sigma-models: a survey

Jonathan Evans (DAMTP Cambridge)

Tuesday 26th February, 2008 15:00-16:00 Mathematics Building, room 516


Sigma models are two-dimensional field theories with interactions defined geometrically in terms of a target manifold; they arise in fields as diverse as condensed matter physics and string theory. Sigma models may be integrable (classically of quantum mechanically) when the target space is a Lie group and there are many generalisations to symmetric spaces, supergroups, or other graded objects. One of the intriguing features of these integrable families is the co-existence of conserved quantities of quite different character. Conventional, local, charges are closely related to well-known integrable hierarchies and, in turn, Toda theories. Non-local charges on the other hand have a less-well-understood, Yangian, structure. I will attempt to summarise some (relatively) recent progress in understanding these things, keeping technicalities to a minimum.

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