Related papers: Novel integrable interpolations
This contribution is based on a talk given by the author at the "Dualities and Generalized Geometries" session of the Corfu Summer Institute 2018 workshops. We overview the results of [1], focusing our attention on integrable…
We prove that the doubly lambda-deformed sigma-models, which include integrable cases, are canonically equivalent to the sum of two single lambda-deformed models. This explains the equality of the exact beta-functions and current anomalous…
Effective field theories for cosmology offer a powerful framework to investigate the dynamics of space--time and address longstanding open puzzles. In this work, we initiate a programme to analyse the ultraviolet completion of…
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…
We use the method of the superpotential to derive exact solutions describing inflationary cosmologies in multi-field models. An example that describes a solution that interpolates between two de Sitter universes is described in detail. New…
We devise three strategies for recognizing admissibility of non-standard inference rules via interpolation, uniform interpolation, and model completions. We apply our machinery to the case of symmetric implication calculus $\mathsf{S^2IC}$,…
Conformal sigma models and WZW models on coset superspaces provide important examples of logarithmic conformal field theories. They possess many applications to problems in string and condensed matter theory. We review recent results and…
We compute the 2- and 3-point functions of currents and primary fields of $\lambda$-deformed integrable $\sigma$-models characterized also by an integer $k$. Our results apply for any semisimple group $G$, for all values of the deformation…
$Vect(N)$, the algebra of vector fields in $N$ dimensions, is studied. Some aspects of local differential geometry are formulated as $Vect(N)$ representation theory. There is a new class of modules, {\it conformal fields}, whose…
We introduce the notion of a classical dihedral affine Gaudin model, associated with an untwisted affine Kac-Moody algebra $\widetilde{\mathfrak{g}}$ equipped with an action of the dihedral group $D_{2T}$, $T \geq 1$ through (anti-)linear…
We consider the $\mathcal{N}=4$ SYM theory with gauge group $Sp(N)$ and the $\mathcal{N}=2$ superconformal field theory consisting of four hypermultiplets in the fundamental representation and one hypermultiplet in the rank-two…
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…
We review some recent developments in the construction of integrable $\eta$- and $\lambda$-deformations of the $AdS_5 \times S^5$ superstring. We highlight their link with Poisson-Lie T-duality.
We show that an integrable four-dimensional non-unitary field theory that was recently proposed as a certain limit of the $\gamma_i$-deformed $\mathcal{N}=4$ SYM theory is incomplete and not conformal -- not even in the planar limit. We…
We construct a new, two-parametric family of integrable models and reveal their underlying duality symmetry. A modular subgroup of this duality is shown to connect non-interacting modes of different systems. We apply the new solution and…
We consider the $\gamma$-deformed $\mathcal{N}=4$ SYM in the double scaling limit of large imaginary twists and small coupling, which discards the gauge fields and retains only certain Yukawa and scalar interactions with three arbitrary…
We introduce a new quasi-isometry invariant, called the divergence spectrum, to study finitely generated groups. We compare the concept of divergence spectrum with the other classical notions of divergence and we examine the divergence…
Nonlinear sigma models appear in a wide variety of physics contexts, such as the long-range order with spontaneously broken continuous global symmetries. There are also large classes of quantum criticality admit sigma model descriptions in…
The compatibility between the conformal symmetry and the closure of conformal algebras is discussed on the nonlinear sigma model. The present approach, above the basis of field redefinition employed in the Hamiltonian scheme, attempts the…
We formulate sufficient conditions for the strong integrability of dressing cosets. We provide several sigma-model backgrounds solving those conditions, some of them are new and some of them were not so far formulated as the dressing…