Related papers: Integrable Sigma Models and Universal Root $T\bar{…

We consider the problem of exact integration of the $T\bar{T}$-deformation of two dimensional quantum field theories, as well as some higher dimensional extensions in the form of $\det T$-deformations. When the action can be shown to only…

This paper deals with higher gradient integrability for $\sigma$-harmonic functions $u$ with discontinuous coefficients $\sigma$, i.e. weak solutions of $\div(\sigma \nabla u) = 0$. We focus on two-phase conductivities, and study the higher…

In this paper we initiate the study of six-dimensional non-linear chiral two-form gauge theories as deformations of free chiral two-form gauge theories driven by stress-tensor $T\overline T$-like flows. To lay the background for this study,…

A key feature of integrable systems is that they can be solved to obtain exact analytical solutions. We show how new models can be constructed through generalisations of some well known nonlinear partial differential equations with…

We give a classification of non-Abelian T-duals of the flat metric in D=4 dimensions with respect to the four-dimensional continuous subgroups of the Poincare group. After dualizing the flat background, we identify majority of dual models…

Using the general method presented by Mohammedi \cite{NM} for the integrability of a sigma model on a manifold, we investigate the conditions for having an integrable deformation of the general sigma model on a manifold with a complex…

We describe a deformation of the principal chiral model (with an even-dimensional target space G) by a B-field proportional to the K\"ahler form on the target space. The equations of motion of the deformed model admit a zero-curvature…

We consider a two-phase Darcy flow in a fractured porous medium consisting in a matrix flow coupled with a tangential flow in the fractures, described as a network of planar surfaces. This flow model is also coupled with the mechanical…

This review is dedicated to two-dimensional sigma models with flag manifold target spaces, which are generalizations of the familiar $CP^{n-1}$ and Grassmannian models. They naturally arise in the description of continuum limits of spin…

The response of an integrable QFT under variation of the Unruh temperature has recently been shown to be computable from an S-matrix preserving (`replica') deformation of the form factor approach. We show that replica-deformed form factors…

We study the evolution of correlation functions of local fields in a two-dimensional quantum field theory under the $\lambda T\bar T$ deformation, suitably regularized. We show that this may be viewed in terms of the evolution of each…

We revisit classical "on shell" duality, i.e., pseudoduality, in two dimensional conformally invariant classical sigma models and find some new interesting results. We show that any two sigma models that are "on shell" duals have opposite…

We look for 3-dimensional Poisson-Lie dualizable sigma models that satisfy the vanishing beta-function equations with constant dilaton field. Using the Poisson-Lie T-plurality we then construct 3-dimensional sigma models that correspond to…

A discrete analogue of the dressing method is presented and used to derive integrable nonlinear evolution equations, including two infinite families of novel continuous and discrete coupled integrable systems of equations of nonlinear…

We construct integrable deformations of the $\lambda$-type for asymmetrically gauged WZW models. This is achieved by a modification of the Sfetsos gauging procedure to account for a possible automorphism that is allowed in $G/G$ models. We…

We introduce and study a class of two-dimensional integrable quantum field theories that carry an internal $\mathbb{Z}_n$ structure. These models extend factorised scattering beyond the conventional framework, featuring both the usual…

We explore dualities and solution-generating transformations in various contexts. Our focus is on the T-duality invariant form of supergravity known as double field theory, the $SL(5)$-invariant M-theory extended geometry, and metrics dual…

This paper has studied the three-dimensional Dunkl oscillator models in a generalization of superintegrable Euclidean Hamiltonian systems to curved ones. These models are defined based on curved Hamiltonians, which depend on a deformation…

Dimensional reduction in two dimensions of gravity in higher dimension, or more generally of d=3 gravity coupled to a sigma-model on a symmetric space, is known to possess an infinite number of symmetries. We show that such a bidimensional…

This study introduces a new unified structural framework for orbifold sigma models that incorporates twisted sectors, singularities, and smooth regions into a single algebraic object. Traditional approaches to orbifold theories often treat…