Related papers: All-loop correlators of integrable $\lambda$-defor…
We study what we call the all-loop anisotropic bosonized Thirring sigma model. This interpolates between the WZW model and the non-Abelian T-dual of the principal chiral model for a simple group. It has an invariance involving the inversion…
We study Penner type matrix models in relation with the Nekrasov partition function of four dimensional \mathcal{N}=2, SU(2) supersymmetric gauge theories with N_F=2,3 and 4. By evaluating the resolvent using the loop equation for general…
We show that two-dimensional sigma models are equivalent to certain perturbed conformal field theories. When the fields in the sigma model take values in a space G/H for a group G and a maximal subgroup H, the corresponding conformal field…
We propose an integrability approach for planar three-point functions at finite coupling in $\mathcal{N}=2$ superconformal field theories obtained as $\mathbb{Z}_K$ orbifolds of $\mathcal{N}=4$ super Yang-Mills (SYM). Generalizing the…
The worldsheet theories that describe Poisson-Lie T-dualisable $\sigma$-models on group manifolds as well as integrable $\eta$, $\lambda$ and $\beta$-deformations provide examples of ${\cal E}$-models. Here we show how such ${\cal…
We invent a method that exploits the geometry in the space of couplings and the known all-loop effective action, in order to calculate the exact in the couplings anomalous dimensions of composite operators for a wide class of integrable…
Let $\mathcal{D}=\left(\mathcal{P},\mathcal{B} \right)$ be a symmetric $2$-$(v,k,\lambda )$ design admitting a flag-transitive, point-imprimitive automorphism group $G$ that leaves invariant a non-trivial partition $\Sigma$ of…
We study the effect of marginal and irrelevant deformations on the renormalization of operators near a CFT fixed point. New divergences in a given operator are determined by its OPE with the operator D that generates the deformation. This…
We discuss some applications of the Morse-Novikov theory to some problems in modern physics, where appears a non-exact closed 1-form $\omega$ (a multi-valued functional). We focus mainly our attention to the cohomology of the de Rham…
In two recent papers we have proposed a program of study which allows us to compute the correlation functions of local and semi-local fields in generalised $\mathrm{T}\bar{\mathrm{T}}$-deformed integrable quantum field theories. This new…
This is a review aimed at a physics audience on the relation between Poisson sigma models on surfaces with boundary and deformation quantization. These models are topological open string theories. In the classical Hamiltonian approach, we…
We present two maximally superintegrable Hamiltonian systems ${\cal H}_\lambda$ and ${\cal H}_\eta$ that are defined, respectively, on an $N$-dimensional spherically symmetric generalization of the Darboux surface of type III and on an…
The link between 3D spaces with (in general, non-constant) curvature and quantum deformations is presented. It is shown how the non-standard deformation of a sl(2) Poisson coalgebra generates a family of integrable Hamiltonians that…
We give a new lower bound on the number of connected components of the space of representations of a surface group into the group of orientation preserving homeomorphisms of the circle. Precisely, for the fundamental group of a genus g…
We construct a $\mathcal{PT}$-symmetric Richardson--Gaudin models for spin-$\tfrac{1}{2}$ systems by deforming the closed integrable Hamiltonian through complex-valued transverse magnetic fields and coupling constants. By defining parity as…
The essential features of a quantum group deformation of classical symmetries of General Relativity in the case with non-vanishing cosmological constant $\Lambda$ are presented. We fully describe (anti-)de Sitter non-commutative spacetimes…
We have computed the simplest five point function in $\mathcal{N} = 4$ SYM at two loops using the hexagonalization approach to correlation functions. Along the way we have determined all two-particle mirror contributions at two loops and we…
Certain two and three point functions of gauge invariant primary operators of ${\cal N}=4$ SYM are computed in ${\cal N}=1$ superspace keeping all the $\th$-components. This allows one to read off many component descendent correlators. Our…
The study of the scaling limit of two-dimensional models of statistical mechanics within the framework of integrable field theory is illustrated through the example of the RSOS models. Starting from the exact description of regime III in…
We present the reduction of the correlation functions of the Ising model on the anisotropic square lattice to complete elliptic integrals of the first, second and third kind, the extension of Kramers-Wannier duality to anisotropic…