Related papers: Double and cyclic $\lambda$-deformations and their…
We collect a number of elementary constructions of $\Z_2$ harmonic $1$-forms, and of families of these objects. These examples show that the branching set $\Sigma$ of a $\Z_2$ harmonic 1-form may exhibit the following features: i) $\Sigma$…
The NSVZ $\beta$ functions in two-dimensional $\mathcal N=(0,2)$ supersymmetric models are revisited. We construct and discuss a broad class of such models using the gauge formulation. All of them represent direct analogs of…
We explore a deformation of the flat space symmetric space sigma model action. The deformed action is designed to allow a Lax connection for the equations of motion, similar to the undeformed model. For this to work, we identify a set of…
The equivalence of several $SL(3)$ sigma models and their special Abelian duals is investigated in the two loop order of perturbation theory. The investigation is based on extracting and comparing various $\beta$ functions of the original…
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…
In recent work, we developed a method to construct invertible and non-invertible symmetries of finite-group gauge theories as topological domain walls on the lattice. In the present work, we consider abelian and non-abelian finite-group…
On a supersymmetric sigma model the covariantly constant forms are related to the conserved currents that are generators of a super W-algebra extending the superconformal algebra. The existence of covariantly constant forms restricts the…
We construct the $\lambda$-model on $SU(3)_k/U(2)_k$ and we compute the one-loop $\beta$-function for the deformation parameter $\lambda$. Its non-compact version for $SU(2,1)_{-k}/U(2)_{-k}$ is also considered, whose target space admits an…
The construction of Non Abelian affine Toda models is discussed in terms of its underlying Lie algebraic structure. It is shown that a subclass of such non conformal two dimensional integrable models naturally leads to the construction of a…
There are 13 equivalence classes of 2D second order quantum and classical superintegrable systems with nontrivial potential, each associated with a quadratic algebra of hidden symmetries. We study the finite and infinite irreducible…
We propose an action for the extended sigma - models in the most general setting of the kinetic term allowed in the nontrivially deformed field - antifield formalism. We show that the classical motion equations do naturally take their…
We generalize the existing works on the way (generalized) LTB models can be embedded into polymerized spherically symmetric models in several aspects. We re-examine such an embedding at the classical level and show that a suitable LTB…
We consider a two-dimensional sigma-model with discrete icosahedral/dodecahedral symmetry. We present high-precision finite-size numerical results that show that the continuum limit of this model is different from the continuum limit of the…
We initiate the study of the interplay between T-duality and classical stress tensor deformations in two-dimensional sigma models. We first show that a general Abelian T-duality commutes with the $T \overline{T}$ deformation, which can be…
Integrable field theories exhibit infinitely many symmetries which underlie their solvability, but the structure of these symmetries can become obscured after performing an integrable deformation such as $\TT$ or an auxiliary field…
Colored lattice models can be used to describe many different types of special functions of interest in both algebraic combinatorics and representation theory, for example Schur polynomials, nonsymmetric Macdonald polynomials, and…
We consider a two $\beta$-ensemble realization of the series of $\beta$-deformed WLZZ matrix models. We demonstrate that such a realization involves $\beta$-deformed Harish-Chandra-Itzykson-Zuber integrals, one of them providing a coupling…
We use world-line methods for pseudo-supersymmetry to construct $sl(2|1)$-invariant actions for the $(2,2,0)$ chiral and ($1,2,1)$ real supermultiplets of the twisted $D$-module representations of the $sl(2|1)$ superalgebra. The derived…
We find the novel class of the supersymmetric deformation of the $\mathbb{CP}^{1}$ $\sigma$-model and its equivalence with the generalised chiral Gross-Neveu. This construction allows the use of field-theoretic techniques and particularly…
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…