A 4D analogue of the Yang-Baxter sigma model is derived from 6D twistor-space Chern-Simons theory via symmetry reduction, with its 2D equations embedded in anti-self-dual Yang-Mills.
Gauge Theory and Integrability, I
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abstract
Several years ago, it was proposed that the usual solutions of the Yang-Baxter equation associated to Lie groups can be deduced in a systematic way from four-dimensional gauge theory. In the present paper, we extend this picture, fill in many details, and present the arguments in a concrete and down-to-earth way. Many interesting effects, including the leading nontrivial contributions to the $R$-matrix, the operator product expansion of line operators, the framing anomaly, and the quantum deformation that leads from $\mathfrak{g}[[z]]$ to the Yangian, are computed explicitly via Feynman diagrams. We explain how rational, trigonometric, and elliptic solutions of the Yang-Baxter equation arise in this framework, along with a generalization that is known as the dynamical Yang-Baxter equation.
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UNVERDICTED 3representative citing papers
Non-commutative 5d Chern-Simons theory on the spinor bundle compactifies to the KP equation, with vanishing tree amplitudes and W_{1+∞} defect algebra reducing to w_{1+∞} in the dispersionless limit.
Integrable deformations of the Breitenlohner-Maison sigma model are obtained from 4d Chern-Simons theory, corresponding to solutions of the homogeneous and inhomogeneous classical Yang-Baxter equations.
citing papers explorer
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The Yang-Baxter Sigma Model from Twistor Space
A 4D analogue of the Yang-Baxter sigma model is derived from 6D twistor-space Chern-Simons theory via symmetry reduction, with its 2D equations embedded in anti-self-dual Yang-Mills.
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Non-Commutative Gauge Theory at the Beach
Non-commutative 5d Chern-Simons theory on the spinor bundle compactifies to the KP equation, with vanishing tree amplitudes and W_{1+∞} defect algebra reducing to w_{1+∞} in the dispersionless limit.
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Integrable Deformations of the Breitenlohner-Maison Model from 4d Chern-Simons Theory
Integrable deformations of the Breitenlohner-Maison sigma model are obtained from 4d Chern-Simons theory, corresponding to solutions of the homogeneous and inhomogeneous classical Yang-Baxter equations.