Related papers: The Courant-Hilbert construction in 4D Chern-Simon…
We present integrable deformations of Yang-Baxter (YB) sigma models based on the Courant-Hilbert (CH) construction. To this end, we employ the four-dimensional Chern-Simons theory, in which the CH construction is shown in arXiv:2509.22080.…
The four-dimensional Chern-Simons (CS) theory provides a systematic procedure for realizing two-dimensional integrable field theories. It is therefore a natural question to ask whether integrable deformations of the theories can be realized…
We study $\eta$-deformations of principal chiral model (PCM) from the viewpoint of a 4D Chern-Simons (CS) theory. The $\eta$-deformed PCM has originally been derived from the 4D CS theory by Delduc, Lacroix, Magro and Vicedo…
In this paper, we shed new light onto $T\bar{T}$-deformations by engineering them on 2D surface defects, supporting chiral and antichiral CFT's, in a 4D Chern-Simons bulk. This approach is motivated by various connections between…
We introduce a new elliptic integrable $\sigma$-model in the form of a two-parameter deformation of the Principal Chiral Model on the group $\text{SL}_{\mathbb{R}}(N)$, generalising a construction of Cherednik for $N=2$ (up to reality…
These lecture notes concern the semi-holomorphic 4d Chern-Simons theory and its applications to classical integrable field theories in 2d and in particular integrable sigma-models. After introducing the main properties of the Chern-Simons…
We construct integrability-preserving deformations of the integrable $\sigma$-model coupling together $N$ copies of the Principal Chiral Model. These deformed theories are obtained using the formalism of affine Gaudin models, by applying…
We develop a unified Courant--Hilbert framework for constructing two-dimensional integrable sigma models deformed by two couplings: a marginal one $\gamma$ and an irrelevant one $\lambda$. The integrability condition is encoded in a…
We study the approaches to two-dimensional integrable field theories via a six-dimensional(6D) holomorphic Chern-Simons theory defined on twistor space. Under symmetry reduction, it reduces to a four-dimensional Chern-Simons theory, while…
We derive integrable deformations of the 2d Breitenlohner-Maison (BM) sigma model that describes the stationary, axisymmetric sector of 4d general relativity, as well as higher-rank generalisations thereof, using the framework of 4d…
In this note we consider the symplectic reduction of a four-dimensional holomorphic Chern-Simons theory recently introduced in arXiv:1908.02289 for describing integrable field theories. We work out explicitly the case of the lambda deformed…
The auxiliary field sigma model (AFSM) has recently been constructed by Ferko and Smith as deformations of the principal chiral model by including auxiliary fields and the potential term given by an arbitrary univariate function. This AFSM…
We study the $\lambda$--deformation of symmetric coset models from the viewpoint of a four dimensional Chern-Simons theory \cite{CY3}. In addition, by applying the "dual" boundary conditions of the ones used in the construction…
Integrable field theories in two dimensions are known to originate as defect theories of 4d Chern-Simons and as symmetry reductions of the 4d anti-self-dual Yang-Mills equations. Based on ideas of Costello, it has been proposed in work of…
A few years ago, some of us devised a method to obtain integrable systems in (2+1)-dimensions from the classical non-Abelian pure Chern-Simons action via reduction of the gauge connection in Hermitian symmetric spaces. In this paper we show…
We present a general construction of integrable degenerate $\mathcal E$-models on a 2d manifold $\Sigma$ using the formalism of Costello and Yamazaki based on 4d Chern-Simons theory on $\Sigma \times \mathbb{C}P^1$. We begin with a…
This paper studies novel four-dimensional integrable field theories that are deformations of self-dual Yang-Mills. They are engineered by considering holomorphic Chern-Simons and BF type theories on covers of twistor space obtained by…
We perform a canonical and BRST analysis of a seven-dimensional Chern-Simons theory on a manifold with boundary. The main result is that the 7D theory induces for consistency a chiral two-form on the 6D boundary. We also comment on similar…
We study the $T\bar{T}$ deformation of the chiral bosons and show the equivalence between the chiral bosons of opposite chiralities and the scalar fields at the Hamiltonian level under the deformation. We also derive the deformed Lagrangian…
We study the $SU(2)$ Principal Chiral Model (PCM) in the presence of an integrable $\eta$-deformation. We put the theory on $\mathbb{R}\times S^1$ with twisted boundary conditions and then reduce the circle to obtain an effective quantum…