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Gauge Theory And Integrability, III
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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.
Forward citations
Cited by 7 Pith papers
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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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Time-Dependent Integrability from Gauge Theory, I
Spacetime-dependent 4d Chern-Simons theory generates time-dependent integrable field theories whose allowed time dependence coincides with one-loop RG flow while preserving Lax integrability.
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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.
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Adjusting Higher Chern-Simons Theory
The authors introduce half-adjusted higher Chern-Simons theories, obtained by a cotangent completion of adjusted L8-algebras, which admit consistent gauge transformations and equations of motion implying full flatness.
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Asymptotic Equivalence Between Quasi-Grammian and Quasi-Wronskian $N$-Soliton Solutions of the Anti-Self-Dual Yang-Mills Equation
Quasi-Grammian and quasi-Wronskian N-soliton solutions of the ASDYM/Yang equation are asymptotically equivalent up to a constant matrix factor, with explicit N-soliton phase shifts.
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Courant-Hilbert deformations of Yang-Baxter sigma models
Yang-Baxter and Courant-Hilbert deformations combine inside 4D Chern-Simons theory: the corrected action equals the master Lagrangian plus half the trace of the energy-momentum tensor.
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Gauge Theory and Integrability: An Overview
A review of the 4d Chern-Simons framework that derives integrable models and Yangian algebras from gauge theory.
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