Theoretical High Energy Seminar by A. Wereszczynski – Niels Bohr Institute - University of Copenhagen

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Theoretical High Energy Seminar by A. Wereszczynski

A. Wereszczynski (Jagellonian University)

Generalized Integrability in Higher Dimensional Classical Theories

I review the concept of generalized zero curvature conditions and integrability in higher dimensions, where integrability is related to the existence of infinitely many conservation laws. I use analogy with the integrability in 1+1 dimensions where the zero curvature condition of Zakharov-Shabat is equivalent to the path independence of the Wilson line operator. Then, the generalized zero curvature condition in higher dimensions is a condition for hyper-surface independence of a hyper-surface ordered operator. I will applied the method to models with two and three dimensional target space and, in particularly, I show that abelian projection of Yang-Mills-dilaton theory is an example of integrable model.