Related papers: Grassmannian sigma model on a finite interval
The paper proposes a variational-inequality based primal-dual dynamic that has a globally exponentially stable saddle-point solution when applied to solve linear inequality constrained optimization problems. A Riemannian geometric framework…
This is a study of the Landau-Ginzburg/Calabi-Yau correspondence, and related matters, using linear sigma models.
We study a three dimensional conformal field theory in terms of its partition function on arbitrary curved spaces. The large $N$ limit of the nonlinear sigma model at the non-trivial fixed point is shown to be an example of a conformal…
The large N limit of the hermitian matrix model in three and four Euclidean space-time dimensions is studied with the help of the approximate Renormalization Group recursion formula. The planar graphs contributing to wave function, mass and…
We propose an inexact Uzawa algorithm with two variable relaxation parameters for solving the generalized saddle-point system. The saddle-point problems can be found in a wide class of applications, such as the augmented Lagrangian…
We introduce a technique for proving all-genus wall-crossing formulas in the gauged linear sigma model as the stability parameter varies, without assuming factorization properties of the virtual class. We implement this technique explicitly…
We introduce in this paper two dimensional lattice models whose continuum limit belongs to the $N=2$ series. The first kind of model is integrable and obtained through a geometrical reformulation, generalizing results known in the $k=1$…
We find a class of fixed point theory for 2- and 3-dimensional non-linear sigma models using Wilsonian renormalization group (WRG) approach. In 2-dimensional case, the fixed point theory is equivalent to the Witten's semi-infinite cigar…
We investigate a global sigma model anomaly in two-dimensional sigma models with Majorana--Weyl fermions coupled to a sigma model field with target space~$G$. The anomaly originates from the nontrivial topology of the space of maps and…
We analyze the dynamics of weakly coupled finite temperature $U(N)$ gauge theories on $S^3$ by studying a class of effective unitary matrix model. Solving Dyson-Schwinger equation at large $N$, we find that different phases of gauge…
In this paper, we propose a variance-reduced primal-dual algorithm with Bregman distance for solving convex-concave saddle-point problems with finite-sum structure and nonbilinear coupling function. This type of problems typically arises in…
We explore the constant curvature holomorphic solutions of the supersymmetric grassmannian sigma model $G(M,N)$ using in particular the gauge invariance of the model. Supersymmetric invariant solutions are constructed via generalizing a…
We construct a mathematical theory of Witten's Gauged Linear Sigma Model (GLSM). Our theory applies to a wide range of examples, including many cases with non-Abelian gauge group. Both the Gromov-Witten theory of a Calabi-Yau complete…
Various effective field theories in four dimensions are shown to have exact non-trivial solutions in the limit as the number $N$ of fields of some type becomes large. These include extended versions of the U(N) Gross-Neveu model, the…
The general prescription for constructing the continuum limit of a field theory is introduced. We then apply the prescription to construct the O(N) non-linear sigma model and the Gross-Neveu model in three dimensions using the large N…
In this work we examine a system consisting of a confined one-dimensional arrangement of atoms that we describe by using the 2-dimensional ${\mathbb C}P^{N-1}$ model, restricted to an interval and at finite temperature. We develop a method…
In this work a method is presented to derive the generating functional in path integral form for a system with an arbitrary number of degrees of freedom and constrained by general conditions. The method is applied to the case of the…
Numerical solutions to the nonlinear sigma model (NLSM), a wave map from 3+1 Minkowski space to S^3, are computed in three spatial dimensions (3D) using adaptive mesh refinement (AMR). For initial data with compact support the model is…
We consider Chern-Simons gauged nonlinear sigma model with boundary which has a manifest bulk diffeomorphism invariance. We find that the Gauss's law can be solved explicitly when the nonlinear sigma model is defined on the Hermitian…
In this paper we explore nonabelian gauged linear sigma models (GLSMs) for symplectic and orthogonal Grassmannians and flag manifolds, checking e.g. global symmetries, Witten indices, and Calabi-Yau conditions, following up a proposal in…