The Courant-Hilbert construction in 4D Chern-Simons theory

Abstract

We consider the Courant-Hilbert (CH) construction of integrable deformations of a two-dimensional principal chiral model (2D PCM) in the context of the four-dimensional Chern-Simons (4D CS) theory. According to this construction, an integrable deformation of 2D PCM is characterized by a boundary function. As a result, the master formula obtained from the 4D CS theory should be corrected by the trace of the energy-momentum tensor so as to support the CH construction. We present some examples of deformation including the $T\bar{T}$-deformation, the root $T\bar{T}$-deformation, the two-parameter mixed deformation, and a logarithmic deformation. Finally, we discuss some generalizations and potential applications of this CH construction.

25 pages; v2: typos corrected, references and some comments added; v3: clarifications and an appendix added, published version in JHEP

References in corpus (33)

• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• On integrability of the Yang-Baxter $\si$-model
• An integrable deformation of the AdS_5 x S^5 superstring action
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• On classical q-deformations of integrable sigma-models
• Jordanian deformations of the AdS_5xS^5 superstring
• Yang-Baxter sigma models based on the CYBE
• Emergence of non-linear electrodynamic theories from $T\bar{T}$-like deformations
• New approach to nonlinear electrodynamics: dualities as symmetries of interaction
• Root-$T\overline{T}$ Deformations in Two-Dimensional Quantum Field Theories
• Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite $\sqrt{T\bar{T}}$ deformations
• N=3 supersymmetric Born-Infeld theory
• A unifying 2d action for integrable $\sigma$-models from 4d Chern-Simons theory
• Duality-Invariant Non-linear Electrodynamics and Stress Tensor Flows
• On the Classical Integrability of Root-$T\overline{T}$ Flows
• Nonlinear automorphism of the conformal algebra in 2D and continuous $\sqrt{T\bar{T}}$ deformations
• Thermodynamic geometry and complexity of black holes in theories with broken translational invariance
• 4-dimensional Chern-Simons theory and integrable field theories
• Bispinor Auxiliary Fields in Duality-Invariant Electrodynamics Revisited
• Twistors, the ASD Yang-Mills equations, and 4d Chern-Simons theory
• 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
• Infinite Family of Integrable Sigma Models Using Auxiliary Fields
• Integrable degenerate $\mathcal{E}$-models from 4d Chern-Simons theory
• The Faddeev-Reshetikhin model from a 4D Chern-Simons theory
• Yang-Baxter deformations of the AdS${}_5\times$S${}^5$ supercoset sigma model from 4D Chern-Simons theory
• Holomorphic Chern-Simons theory and lambda models: PCM case
• $\lambda$-deformed $Ad{S}_5\times S^5$ superstring from 4D Chern-Simons theory
• Lax Connections in $T\bar{T}$-deformed Integrable Field Theories
• Integrable deformed $T^{1,1}$ sigma models from 4D Chern-Simons theory
• Non-Abelian Toda field theories from a 4D Chern-Simons theory
• 4D Chern-Simons theory with auxiliary fields

Cited by in corpus (1)

• Integrable models from 4d holomorphic BF theory