Related papers: Two dimensional non-linear sigma models as a limit…

The dual of the four dimensional non-linear sigma model is constructed using techniques familiar to string theory. This construction necessitates the introduction of a rank two antisymmetric tensor field whose properties are examined. The…

Using the effective potential, the large-$N$ nonlinear $O(N)$ sigma model with the curvature coupled term is studied on $S^2\times R^1$. We show that, for the conformally coupled case, the dynamical mass generation of the model in the…

By using the results of a high-statistics (O(10^7) measurements) Monte Carlo simulation we test several predictions of perturbation theory on the O(n) non-linear sigma-model in 2 dimensions. We study the O(3) and O(8) models on large enough…

The aim of this paper is to investigate the non-relativistic limit of integrable quantum field theories with fermionic fields, such as the O(N) Gross-Neveu model, the supersymmetric Sinh-Gordon and non-linear sigma models. The…

We discuss the two-dimensional Grassmannian sigma model $\mathbb{G}_{N, M}$ on a finite interval $L$. The different boundary conditions which allow to obtain analytical solutions by the saddle-point method in the large $N$ limit are…

We study dualities in off-shell 4D N = 2 supersymmetric sigma-models, using the projective superspace approach. These include (i) duality between the real O(2n) and polar multiplets; and (ii) polar-polar duality. We demonstrate that the…

The (2+1) dimensional gauged O(3) nonlinear sigma model with Chern-Simons term is canonically quantized. Furthermore, we study a nonminimal coupling in this model implemented by means of a Pauli-type term. It is shown that the set of…

We consider a general class of two-dimensional spin systems, with continuous but not necessarily smooth, possibly long-range, $O(N)$-symmetric interactions, for which we establish algebraically decaying upper bounds on spin-spin…

According to the standard classification of Conformal Quantum Field Theory (CQFT) in two dimensions, the massless continuum limit of the $O(2)$ model at the Kosterlitz-Thouless (KT) transition point should be given by the massless free…

Recently, the author has constructed a series of four dimensional non-critical string theories with eight supercharges, dual to theories of light electric and magnetic charges, for which exact formulas for the central charge of the…

We continue the study, initiated in arXiv:1404.1094, of the $O(N)$ symmetric theory of $N+1$ massless scalar fields in $6-\epsilon$ dimensions. This theory has cubic interaction terms $\frac{1}{2}g_1 \sigma (\phi^i)^2 + \frac{1}{6}g_2…

We analyze the two-dimensional CP(N-1) sigma model defined on a finite space interval L, with various boundary conditions, in the large N limit. With the Dirichlet boundary condition at the both ends, we show that the system has a unique…

In this paper we consider matrix and vector models in the large N limit ($N \times N$ matrices and vectors with N^{2} components). For the case of zero-dimensional model (D=0) it is proved that in the strong coupling limit $g \to \infty$…

Using Wilsonian methods, we study the renormalization group flow of the Nonlinear Sigma Model in any dimension $d$, restricting our attention to terms with two derivatives. At one loop we always find a Ricci flow. When symmetries completely…

The 1/N expansion for the O(N) vector model in four dimensions is reconsidered. It is emphasized that the effective potential for this model becomes everywhere complex just at the critical point, which signals an unstable vacuum. Thus a…

We conjecture that the $O(N)$-symmetric non-linear sigma model in the semi-infinite $(1+1)$-dimensional space is ``integrable'' with respect to the ``free'' and the ``fixed'' boundary conditions. We then derive, for both cases, the boundary…

We continue the analysis started in a recent paper of the large-N two-dimensional CP(N-1) sigma model, defined on a finite space interval L with Dirichlet (or Neumann) boundary conditions. Here we focus our attention on the problem of the…

N = 2 supersymmetry in four space-time dimensions is intimately related to hyperkahler and quaternionic Kahler geometries. On one hand, the target spaces for rigid supersymmetric sigma-models are necessarily hyperkahler manifolds. On the…

We develop superspace techniques to construct general off-shell N=1,2,3,4 superconformal sigma-models in three space-time dimensions. The most general N=3 and N=4 superconformal sigma-models are constructed in terms of N=2 chiral…

The large-$N$ nonlinear $O(N)$, $CP^{N-1}$ $\sigma$ models are studied on $R^2 \times S^1$. The $N$-components scalar fields of the models are supposed to acquire a phase $e^{i2\pi\delta}$ $(0\leq \delta <1)$, along the circulation of the…