For the root-of-unity XXZ chain, non-commuting transfer matrices generate an explicit Onsager algebra and duality defects obeying Z_N Tambara–Yamagami fusion rules.
Gauge Theory and Integrability, I
5 Pith papers cite this work. Polarity classification is still indexing.
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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.
representative 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.
Derives integrable deformations of the BM sigma model from 4d Chern-Simons theory via Cole-Weck model deformations linked to homogeneous and inhomogeneous classical Yang-Baxter equations.
Intersecting surface operators in 6d holomorphic Chern-Simons and BF theories produce local R-matrix-like operators with evidence for Yang-Baxter relations and derived coproducts from OPEs.
Twistor-space 6d Chern-Simons theory with Yang-Baxter boundary conditions yields a 4d integrable field theory whose symmetry reduction is the 2d Yang-Baxter sigma model.
citing papers explorer
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Lattice non-invertible symmetry from non-commuting transfer matrices
For the root-of-unity XXZ chain, non-commuting transfer matrices generate an explicit Onsager algebra and duality defects obeying Z_N Tambara–Yamagami fusion rules.
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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
Derives integrable deformations of the BM sigma model from 4d Chern-Simons theory via Cole-Weck model deformations linked to homogeneous and inhomogeneous classical Yang-Baxter equations.
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Intersecting Surface Operators in 6d Holomorphic Field Theories
Intersecting surface operators in 6d holomorphic Chern-Simons and BF theories produce local R-matrix-like operators with evidence for Yang-Baxter relations and derived coproducts from OPEs.
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The Yang-Baxter Sigma Model from Twistor Space
Twistor-space 6d Chern-Simons theory with Yang-Baxter boundary conditions yields a 4d integrable field theory whose symmetry reduction is the 2d Yang-Baxter sigma model.