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, II
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abstract
Starting with a four-dimensional gauge theory approach to rational, elliptic, and trigonometric solutions of the Yang-Baxter equation, we determine the corresponding quantum group deformations to all orders in $\hbar$ by deducing their RTT presentations. The arguments we give are a mix of familiar ones with reasoning that is more transparent from the four-dimensional gauge theory point of view. The arguments apply most directly for $\mathfrak{gl}_N$ and can be extended to all simple Lie algebras other than $\mathfrak{e}_8$ by taking into account the self-duality of some representations, the framing anomaly for Wilson operators, and the existence of quantum vertices at which several Wilson operators can end.
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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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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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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.