Infinitesimal moduli for the Strominger system and Killing spinors in generalized geometry

复超球面上的微分共形刚性构造性方法

A Constructive Approach to Infinitesimal Conformal Rigidity on Complex Hyperbolic Space

本文通过局部分析和构造性方法证明复超球面上的共形向量场为Killing向量场，并扩展到任意维数。

On a new class of infinitesimal group actions on pseudo-Riemannian manifolds

Using the Lie derivative of the metric we define a class of Lie algebras of vector fields by generalising the concept of Killing vectors. As a Lie algebra they define locally a group action on the pseudo-Riemannian manifold through exponentiation. The motivation behind studying these infinitesimal group actions is the investigation of $\mathcal{I}$-degenerate pseudo-Riemannian spaces, i.e., spaces having identical polynomial curvature invariants. In particular, we show that all the known examples of $\mathcal{I}$-degenerate pseudo-Riemannian spaces possess such vector fields.

沿曲线的无穷小等距与广义Jacobi方程

Infinitesimal isometries along curves and generalized Jacobi equations

定义了黎曼流形M上沿测地线的Jacobi场.我们将这一概念推广到任意平滑曲线，称之为沿曲线的无穷小等距。我们给出两种方法：1）计算Killing方程的完全延拓，然后限制到曲线上; 2）计算曲线刚体运动的变分方程。这导致沿着曲线的Killing输运，其是射流束J（TM）上的相关连接的平行输运。我们研究了这种联系的曲率和完整性。特别地，在二维中，曲率是M上无穷小等距的局部障碍。

Finsler几何中Killing向量场的十二种刻画

Twelve characterisations of Killing vector fields in Finsler geometry

本文在Finsler几何中利用Frölicher-Nijenhuis形式体系，建立了Killing向量场的十二种等价刻画，并给出局部方程形式，揭示其多方面的几何本质。

广义自旋流形的Killing（超）代数

Killing (super)algebras for generalised spin manifolds

研究为广义自旋结构相关旋量丛联络定义Killing（超）代数，纳入特定元素，证明其为庞加莱超代数扩展的过滤子变形，通过斯宾塞上同调确定所属变形子类，还能重构超对称背景几何为齐性空间。

Killing旋量是黎曼超几何中的Killing向量场

Killing spinors are Killing vector fields in Riemannian Supergeometry

超流形M与任意伪黎曼自旋流形（M_0，g_0）正则相关.将度量g_0推广到T_p M，p \in M_0上的双线性型g（p）的域g，（M，g）的伪黎曼超几何被表示为M上的G-结构，其中G是具有偶部分G_0 \cong Spin（k，l）的超群，（k，l）是（M_0，g_0）的签名.根据定义，（M，g）上的Killing向量场是这个G-结构的无穷小自同构。对于每个旋量场s，M上存在一个相应的奇向量场X_s。我们的主要结果是：X_s是（M，g）上的Killing向量场当且仅当s是扭量旋量。特别地，任何Killing旋量s定义一个Killing向量场X_s。

The CR Killing operator and Bernstein-Gelfand-Gelfand construction in CR geometry

We elaborate the tractor calculus for compatible almost CR structures (also known as strictly pseudoconvex partially integrable almost CR structures) on contact manifolds, and as an application, express the first BGG invariant differential operator $D_0$ explicitly in some cases, i.e., for some tractor connections. An interesting outcome is the fact that the "modified" adjoint tractor connection $\tilde{\nabla}$ governing infinitesimal deformations of parabolic geometries generates what we call the CR Killing operator as its first BGG operator, and actually, it does not agree with the first BG…

Infinitesimal isometries of connection metric and generalized moment map equation

Let $(M,g)$ be a smooth Riemannian manifold, $K$ a compact Lie group and $p:P\to M$ a principal $K$-bundle over $M$ endowed with a connection $A$. Fixing a bi invariant inner product on Lie algebra $\mathfrak{k}$ of $K$, the connection $A$ and metric $g$ define a Riemannian metric $g_A$ on $P$. Let $\tilde {X}$ be the horizontal lift of vector field $X$ on $M$ and, let $ξ^ν$ be the vertical field associated with section $ν\in A^0(\mathrm{ad}( P))$ of the adjoint bundle. It is proved that the connection $A$ is invariant under the 1-parameter group of local diffeomorphism generated by $\tilde{ X…

弦李代数的规范理论

Gauge theory for string algebroids

本文提出了一种弦李代数的规范理论，通过内自同构描述哈密顿作用，并证明了Calabi系统解的模空间具有伪Kähler度量及拓扑公式。

Moduli in General $SU(3)$-Structure Heterotic Compactifications

In this thesis, we study moduli in compactifications of ten-dimensional heterotic supergravity. We consider supersymmetric compactifications to four-dimensional maximally symmetric space, commonly referred to as the Strominger system. The compact part of space-time $X$ is a six-dimensional manifold of what we refer to as a heterotic $SU(3)$-structure. We show that this system can be put in terms of a holomorphic operator $\bar D$ on a bundle $\mathcal{Q}=T^*X\oplus\mathrm{End}(TX)\oplus\mathrm{End}(V)\oplus TX$, defined by a series of extensions. We proceed to compute the infinitesimal deforma…

Holomorphic Bundles and the Moduli Space of N=1 Supersymmetric Heterotic Compactifications

We describe the first order moduli space of heterotic string theory compactifications which preserve $N=1$ supersymmetry in four dimensions, that is, the infinitesimal parameter space of the Strominger system. We establish that if we promote a connection on $TX$ to a field, the moduli space corresponds to deformations of a holomorphic structure $\bar D$ on a bundle $\cal Q$. The bundle $\cal Q$ is constructed as an extension by the cotangent bundle $T^*X$ of the bundle $E= {\rm End}(V) \oplus {\rm End}(TX) \oplus TX$ with an extension class $\cal H$ which precisely enforces the anomaly cancela…

异质SU(3)模空间的局部描述

Local descriptions of the heterotic SU(3) moduli space

本文研究异质弦理论中Hull-Strominger系统模空间的局部结构，通过形变复形和上同调同构证明其预期维数为零，并提供Dolbeault型定理连接Čech上同调。