3-dimensional mixed BF theory and Hitchin's integrable system

Abstract

The affine Gaudin model, associated with an untwisted affine Kac-Moody algebra, is known to arise from a certain gauge fixing of 4-dimensional mixed topological-holomorphic Chern-Simons theory in the Hamiltonian framework. We show that the finite Gaudin model, associated with a finite-dimensional semisimple Lie algebra, or more generally the tamely ramified Hitchin system on an arbitrary Riemann surface, can likewise be obtained from a similar gauge fixing of 3-dimensional mixed BF theory in the Hamiltonian framework.

References in corpus (34)

• Gaudin Model, Bethe Ansatz and Critical Level
• Anharmonic oscillators, the thermodynamic Bethe ansatz, and nonlinear integral equations
• Spectral determinants for Schroedinger equation and Q-operators of Conformal Field Theory
• Gauge Theory and Integrability, II
• Gauge Theory and Integrability, I
• Hitchin Systems - Symplectic Hecke Correspondence and Two-dimensional Version
• Supersymmetric gauge theory and the Yangian
• Gaudin models with irregular singularities
• Opers with irregular singularity and spectra of the shift of argument subalgebra
• Quantum Sine(h)-Gordon Model and Classical Integrable Equations
• A unifying 2d action for integrable $\sigma$-models from 4d Chern-Simons theory
• Assembling integrable sigma-models as affine Gaudin models
• Gauge Theory And Integrability, III
• Integrable coupled sigma-models
• The Chern-Simons Origin of Superstring Integrability
• Higher-level eigenvalues of Q-operators and Schroedinger equation
• Comments on $\eta$-deformed principal chiral model from 4D Chern-Simons theory
• On the Zakharov-Mikhailov action: $4$d Chern-Simons origin and covariant Poisson algebra of the Lax connection
• Integrable deformations of coupled sigma-models
• New integrable coset sigma models
• Yang-Baxter deformations of the AdS${}_5\times$S${}^5$ supercoset sigma model from 4D Chern-Simons theory
• The Faddeev-Reshetikhin model from a 4D Chern-Simons theory
• Integrable models with twist function and affine Gaudin models
• Holomorphic Chern-Simons theory and lambda models: PCM case
• $\lambda$-deformed $Ad{S}_5\times S^5$ superstring from 4D Chern-Simons theory
• Cyclotomic Gaudin models: construction and Bethe ansatz
• Non-Abelian Toda field theories from a 4D Chern-Simons theory
• Integrable deformed $T^{1,1}$ sigma models from 4D Chern-Simons theory
• Lax formulation for harmonic maps to a moduli of bundles
• Symmetric space $\lambda$-model exchange algebra from 4d holomorphic Chern-Simons theory
• Cyclotomic Gaudin models with irregular singularities
• A one-loop exact quantization of Chern-Simons theory
• Classical $N$-Reflection Equation and Gaudin Models
• Comments on $\lambda$--deformed models from 4D Chern-Simons theory

Cited by in corpus (3)

• Lagrangian multiforms on coadjoint orbits for finite-dimensional integrable systems
• 4D Chern-Simons theory with auxiliary fields
• Integrable models from 4d holomorphic BF theory