Gauge Theory And Integrability, III

• DOI: 10.48550/arxiv.1908.02289
• Publication Date: 2019-01-01
• Authors: Costello, Kevin; Yamazaki, Masahito
• Keywords: High Energy Physics - Theory; Nonlinear Sciences - Exactly Solvable and Integrable Systems; High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech); 0103 physical sciences; FOS: Physical sciences; Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI); 01 natural sciences; Condensed Matter - Statistical Mechanics; Mathematical Physics

108 pages, 19 figures<br/>We study two-dimensional integrable field theories from the viewpoint of the four-dimensional Chern-Simons-type gauge theory introduced recently. The integrable field theories are realized as effective theories for the four-dimensional theory coupled with two-dimensional surface defects, and we can systematically compute their Lagrangians and the Lax operators satisfying the zero-curvature condition. Our construction includes many known integrable field theories, such as Gross-Neveu models, principal chiral models with Wess-Zumino terms and symmetric-space coset sigma models. Moreover we obtain various generalization these models in a number of different directions, such as trigonometric/elliptic deformations, multi-defect generalizations and models associated with higher-genus spectral curves, many of which seem to be new.<br/>