Related papers: Integrable double deformation of the principal chi…
We systematically classify all supersymmetry-preserving mass deformations of SYM matrix models in all dimensions (D = 3, 4, 6, 10). In D = 10, the polarized IKKT model emerges as the only possible deformation. In D = 4, we identify two…
A master equation expressing the classical integrability of two-dimensional non-linear sigma models is found. The geometrical properties of this equation are outlined. In particular, a closer connection between integrability and T-duality…
We introduce a two-parameter deformation of 2x2 matrices without imposing any condition on the matrices and give the universal R-matrix of the nonstandard quantum group which satisfies the quantum Yang-Baxter relation. Although in the…
We study integrable deformations of two-dimensional non-linear sigma-models and present a new class of classical solutions to critical bi-Yang-Baxter models for general groups. For the simplest example, namely the SL(2,R) bi-Yang-Baxter…
Duality properties of the $SU(2)$ Principal Chiral Model are investigated starting from a one-parameter family of its equivalent Hamiltonian descriptions generated by a non-Abelian deformation of the cotangent space $T^*SU(2) \simeq SU(2)…
It turns out that many integrable $\sigma$-models on group manifolds belong to the class of the so-called ${ \mathcal E}$-models which are relevant in the context of the Poisson-Lie T-duality. We show that this is the case also for the…
The chiral geometry of the multiple chiral doublet bands with identical configuration is discussed for different triaxial deformation parameters $\gamma$ in the particle rotor model with $\pi h_{11/2}\otimes \nu h_{11/2}^{-1}$. The energy…
We construct a generalisation of the $\lambda$-deformation of the Principal Chiral Model (PCM) where we deform just a subgroup $F$ of the full symmetry group $G$. We find that demanding Lax integrability imposes a crucial restriction,…
Motivated by a system consisting of a number of parallel M5-branes, we study possible local deformations of a chiral two-form in six dimensions. Working to first order in the coupling constant, this reduces to the study of the local BRST…
We consider classical and quantum integrable sigma models and their relations with the solutions of renormalization group equations. We say that an integrable sigma model possesses the "nice" duality property if the dual quantum field…
Integrable deformation of SU(2) sigma and lambda models are considered at the classical and quantum levels. These are the Yang-Baxter and XXZ-type anisotropic deformations. The XXZ type deformations are UV safe in one regime, while in…
We study the chiral two-matrix model with polynomial potential functions $V$ and $W$, which was introduced by Akemann, Damgaard, Osborn and Splittorff. We show that the squared singular values of each of the individual matrices in this…
It is argued that, in the two dimensional principal chiral model, the Wess-Zumino term can be induced quantum mechanically, allowing the model with the critical value of the coupling constant $\lambda^2 = 8\pi/|k|$ to turn into the…
Two-dimensional $\sigma$-models with $\mathbb{Z}_N$-symmetric homogeneous target spaces have been shown to be classically integrable when introducing WZ-terms in a particular way. This article continues the search for new models of this…
Principal chiral models on a d-1 dimensional simplex are introduced and studied analytically in the large $N$ limit. The $d = 0, 2, 4$ and $\infty$ models are explicitly solved. Relationship with standard lattice models and with few-matrix…
Recently, for principal chiral models and symmetric coset sigma models, Hoare and Tseytlin proposed an interesting conjecture that the Yang-Baxter deformations with the homogeneous classical Yang-Baxter equation are equivalent to…
The Yang-Baxter $\sigma$-model is a systematic way to generate integrable deformations of AdS$_5\times$S$^5$. We recast the deformations as seen by open strings, where the metric is undeformed AdS$_5\times$S$^5$ with constant string…
We point out the existence of nonlinear $\sigma$-models on group manifolds which are left symmetric and right Poisson-Lie symmetric. We discuss the corresponding rich T-duality story with particular emphasis on two examples: the anisotropic…
A covariant formalism for Moyal deformations of gauge theory and differential equations which determine Seiberg-Witten maps is presented. Replacing the ordinary product of functions by the noncommutative Moyal product, noncommutative…
We study the noncommutative extensions of certain integrable field theories, namely the sine- and sinh-Gordon (sG and shG) models, and the U(N) principal chiral model (pcm). We argue that the Moyal deformations of the sG and shG models are…