Related papers: Grassmannian sigma model on a finite interval

In this short note we will revisit the large $N$ solution of $\mathbb{C}P^N$ sigma model on a finite interval of length $L$. We will find a family of boundary conditions for which the large $N$ saddle point can be found analytically. For a…

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…

We discuss the two-dimensional Grassmannian $SU(N)/S(U(N-2)\times U(2))$ and the flag $SU(N)/S(U(N-2)\times U(1)\times U(1))$ sigma models on a finite interval and construct analytical solutions of gap equations in the large N limit. We…

We study the $O(N)$ non-linear $\sigma$ model on three-dimensional manifolds of constant curvature by means of the large $N$ expansion at the critical point. We examine saddle point equations imposing anti-periodic boundary condition in…

This is the third of the series of articles on the large-$N$ two-dimensional $\mathbb{CP}^{N-1}$ sigma model, defined on a finite space interval $L$ with Dirichlet boundary conditions. Here the cases of the general Dirichlet boundary…

In the context of integrable field theory with boundary, the integrable non-linear sigma models in two dimensions, for example, the $O(N)$, the principal chiral, the ${\rm CP}^{N-1}$ and the complex Grassmannian sigma models are discussed…

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…

In this paper, we study three dimensional NL$\sigma$Ms within two kind of nonperturbative methods; WRG and large-N expansion. First, we investigate the renormalizability of some NL$\sigma$Ms using WRG equation. We find that some models have…

The CP(N-1) \sigma\ model on finite interval of length R with Dirichlet boundary conditions is analysed in the 1/N expansion. The theory has two phases, separated by a phase transition at R ~ 1/\Lambda, \Lambda\ is dynamical scale of the…

We study an N=1 two-dimensional non-linear sigma model with boundaries representing, e.g., a gauge fixed open string. We describe the full set of boundary conditions compatible with N=1 superconformal symmetry. The problem is analyzed in…

We study the topological-antitopological fusion equations for supersymmetric sigma models on Grassmannian manifolds G(k,N). We find a basis in which the metric becomes diagonal and the $tt^*$ equations become tractable. The solution for the…

Invariant correlation functions for ${\rm SO}(1,N)$ hyperbolic sigma-models are investigated. The existence of a large $N$ asymptotic expansion is proven on finite lattices of dimension $d \geq 2$. The unique saddle point configuration is…

We first consider nonlinear Grassmann sigma models in any dimension and next construct their submodels. For these models we construct an infinite number of nontrivial conserved currents. Our result is independent of time-space dimensions…

This article studies large $N$ limits of a coupled system of $N$ interacting $\Phi^4$ equations posed over $\mathbb{T}^{d}$ for $d=2$, known as the $O(N)$ linear sigma model. Uniform in $N$ bounds on the dynamics are established, allowing…

We study vacua, walls and three-pronged junctions of mass-deformed nonlinear sigma models on $SO(2N)/U(N)$ and $Sp(N)/U(N)$ for generic $N$. We review and discuss the on-shell component Lagrangians of the ${\mathcal{N}}=2$ nonlinear sigma…

We study the stochastic quantization of two-dimensional nonlinear sigma model in the large $N$ limit. Our main tool is the {\it effective} Langevin equation with which we investigate nonperturbative phenomena and derive the results which…

Subject of this work are the applications of a field theoretical model, called here generalized nonlinear sigma model or simply GNLSM,to the dynamics of a chain subjected to constraints. Chains with similar properties and constraints have…

We study the non-minimal supersymmetric heterotically deformed $\mathcal{N}=(0,2)$ sigma model with the Grassmannian target space $\mathcal{G}_{M,N}$. To develop the appropriate superfield formalism, we begin with a simplified model with…

We show how to obtain the O(N) non-linear sigma model in two dimensions as a strong coupling limit of the corresponding linear sigma model. In taking the strong coupling limit, the squared mass parameter must be given a specific coupling…

A model of two-leg spin-S ladder with two additional frustrating diagonal exchange couplings J_{D}, J_{D}' is studied within the framework of the nonlinear sigma model approach. The phase diagram has a rich structure and contains 2S gapless…