A four-dimensional Chern-Simons gauge theory with surface defects systematically engineers two-dimensional integrable field theories with Lax operators.
Review of AdS/CFT Integrability, Chapter II.3: Sigma Model, Gauge Fixing
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abstract
This review is devoted to the classical integrability of the AdS5xS5 superstring theory. It starts with a reminder of the corresponding action as a coset model. The symmetries of this action are then reviewed. The classical integrability is then considered from the lagrangian and hamiltonian points of view. The second part of this review deals with the gauge fixing of this theory. Finally, some aspects of the pure spinor formulation are also briefly reviewed.
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Gauge Theory And Integrability, III
A four-dimensional Chern-Simons gauge theory with surface defects systematically engineers two-dimensional integrable field theories with Lax operators.