Non-ultralocality, affine Gaudin models and ODE/IM

Benoit Vicedo (University of York)

Tuesday 12th November 16:00-17:00 Maths 311B

Abstract

Non-ultralocality is a long-standing open problem in classical integrable field theory which has precluded the first-principle quantisation of many important models. I will review a recent proposal for dealing with this issue, which relates it to the study of quantum Gaudin models associated with affine Kac-Moody algebras. Although comparatively little is presently known about quantum Gaudin models in affine type, the description of the spectrum of the integrals of motion in finite type quantum Gaudin models is very well understood and has a deep connection to the geometric Langlands correspondence. I will go on to review recent progress towards constructing the local integrals of motion in quantum Gaudin models in affine type, based on joint work with Sylvain Lacroix and Charles Young, which draws closely on the analogy with the well understood case of finite type. I will argue that all these results suggest there is a close connection between the problem of non-ultralocality and the ODE/IM correspondence.

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