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DTSTAMP:20261110T041002Z
UID:43fa4e6a-a0bb-4136-992d-2d1dca471fa5
DTSTART:20261111T150000
DTEND:20261111T163000
DESCRIPTION:Two-dimensional integrable field theories exhibit a collection 
 of rich algebraic properties: They possess a Lax connection\, whose monodr
 omy generates infinitely many conserved charges\, a Maillet bracket\, orga
 nised by a twist function and many admit a description in terms of Kac-Moo
 dy currents via Affine Gaudin models. In this talk we will describe recent
  work which attempts to give a higher-dimensional origin for these feature
 s. Using the covariant phase space formalism\, we study six-dimensional ho
 lomorphic Chern–Simons theory on twistor space\, from which many of thes
 e models descend. From the symplectic structure one readily attains a Taki
 ff-type algebra on the four dimensional defects which\, once a gauge redun
 dancy is removed\, gives a four-dimensional analogue of the Maillet bracke
 t. For the four-dimensional WZW model we make this explicit\, including re
 covering the Maillet bracket of the principal chiral model with a Wess–Z
 umino term upon reduction to two dimensions. Finally\, using the geometry 
 of a CR-foliation of twistor space we will describe a four-dimensional ana
 logue of the monodromy\, the Cauchy  transport operator\, in which the Cau
 chy kernel replaces path ordering\, and describe its quadratic Poisson alg
 ebra and symmetric regularisation. \n\nThis talk is based on work with D. 
 Chatzis\, J. Stedman and D. C. Thompson.
LOCATION:ETH Zürich\, Hönggerberg HIT E 41.1
ORGANIZER:Ryan Cullinan
SUMMARY:Integrable structures from twistor space: a Hamiltonian perspective
  on holomorphic Chern–Simons theory
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