Description of surfaces associated with Grassmannian sigma models on Minkowski space

Surfaces associated with sigma models and the sine-Gordon equation

We present a unified method of construction of surfaces associated with Grassmannian sigma models, expressed in terms of an orthogonal projector. This description leads to compact formulae for structural equations of two-dimensional surfaces immersed in the su(N) algebra. In the special case of the CP^1 sigma model we obtain constant negative Gaussian curvature surfaces. As a consequence, this leads us to an explicit relation between the CP^1 sigma model and the sine-Gordon equation.

Topological-antitopological fusion and the quantum cohomology of Grassmannians

We suggest an explanation for the part of the Satake Correspondence which relates the quantum cohomology of complex Grassmannians and the quantum cohomology of complex projective space, as well as their respective Stokes data, based on the original physics approach using the tt* equations. We also use the Stokes data of the tt* equations to provide a Lie-theoretic link between particles in affine Toda models and solitons in certain sigma-models. Along the way, we illustrate some (well known) relations between the tt* equations, the non-abelian Hodge Correspondence, and quantum cohomology.

无穷远处的Carrollian与celestial空间

Carrollian and celestial spaces at infinity

本文利用Poincaré群的齐性空间刻画了Minkowski时空渐近无穷远（Spi、Ti及新空间Ni）的几何结构，揭示了其Carrollian不变性、Grassmannian几何特征，并证明了Ni的对称代数同构于BMS代数，且可由渐近几何重构时空。

Flag manifold sigma models: spin chains and integrable theories

This review is dedicated to two-dimensional sigma models with flag manifold target spaces, which are generalizations of the familiar $CP^{n-1}$ and Grassmannian models. They naturally arise in the description of continuum limits of spin chains, and their phase structure is sensitive to the values of the topological angles, which are determined by the representations of spins in the chain. Gapless phases can in certain cases be explained by the presence of discrete 't Hooft anomalies in the continuum theory. We also discuss integrable flag manifold sigma models, which provide a generalization o…

An Anisotropic shrinking flow and L_p Minkowski problem

We consider a shrinking flow of smooth, closed, uniformly convex hypersurfaces in (n+1)-dimensional Euclidean space with speed fu^{alpha}{sigma}_n^{beta}, where u is the support function of the hypersurface, alpha, beta are two constants, and beta>0, sigma_n is the n-th symmetric polynomial of the principle curvature radii of the hypersurface. We prove that the flow has a unique smooth and uniformly convex solution for all time, and converges smoothly after normalisation, to a soliton which is a solution of an elliptic equation, when the constants alpha, beta belong to a suitable range, provid…

Lorentz-Minkowski 3-空间中的模曲面：曲率与应用

Modular Surfaces in Lorentz-Minkowski 3-Space: Curvature and Applications

本文研究 Lorentz-Minkowski 3-空间中模曲面曲率符号与复解析函数零点的关系，完全分类零高斯曲率模曲面，证明非平面极大模曲面不存在，并展示其在共形场论与非线性 sigma 模型中的应用。

超临界对偶 k-Minkowski 流与一般给定数据：先验估计与渐近收敛

Supercritical dual k-Minkowski flows with general prescribed data: a priori estimates and asymptotic convergence

本文研究超临界对偶 k-Minkowski 流的长时间行为，证明其从任意严格凸初始曲面指数收敛到唯一严格凸稳态解，并给出显式收敛速率与唯一性。

A class of anisotropic expanding curvature flows

We consider an expanding flow of smooth, closed, uniformly convex hypersurfaces in (n+1)-dimensional Euclidean space with speed fu^{alpha}{sigma}_k^{beta}, where u is the support function of the hypersurface, alpha, beta are two constants, and beta>0, sigma_k is the k-th symmetric polynomial of the principle curvature radii of the hypersurface, k is an integer and 1<= k<= n. We prove that the flow has a unique smooth and uniformly convex solution for all time, and converges smoothly after normalisation, to a soliton which is a solution of a elliptic equation, when the constants alpha, beta bel…

Loop groups in Yang-Mills theory

We consider the Yang-Mills equations with a matrix gauge group $G$ on the de Sitter dS$_4$, anti-de Sitter AdS$_4$ and Minkowski $R^{3,1}$ spaces. On all these spaces one can introduce a doubly warped metric in the form $d s^2 =-d u^2 + f^2 d v^2 +h^2 d s^2_{H^2}$, where $f$ and $h$ are the functions of $u$ and $d s^2_{H^2}$ is the metric on the two-dimensional hyperbolic space $H^2$. We show that in the adiabatic limit, when the metric on $H^2$ is scaled down, the Yang-Mills equations become the sigma-model equations describing harmonic maps from a two-dimensional manifold (dS$_2$, AdS$_2$ or…

$Sp(8)$ invariant higher spin theory, twistors and geometric BRST formulation of unfolded field equations

We discuss twistor-like interpretation of the $Sp(8)$ invariant formulation of 4d massless fields in ten dimensional Lagrangian Grassmannian $Sp(8)/P$ which is the generalized space-time in this framework. The correspondence space $\mathbf{C}$ is $SpH(8)/PH$ where $SpH(8)$ is the semidirect product of $Sp(8)$ with Heisenberg group $\HG$ and $PH$ is some quasiparabolic subgroup of $SpH(8)$. Spaces of functions on $Sp(8)/P$ and $SpH(8)/PH$ consist of $Q_P $ closed functions on $Sp(8)$ and $Q_{PH} $ closed functions on $SpH(8)$, where $Q_P $ and $Q_{PH}$ are canonical BRST operators of $P$ and $P…