论文标题
带有$ g $结构的字符串压实的几何和超符号代数
The Geometry and Superconformal Algebras of String Compactifications with a $G$-structure
论文作者
论文摘要
在本文中，我们研究了配备有$ G $结构的流形的弦弦压缩，并特别强调了几何与物理学之间的相互作用。我们遵循两种互补方法。在论文的第一部分中，我们采用了Sigma模型的观点，并将重点放在世界表超宪法领域理论上。我们考虑对7维额外扭曲的连接总和（ETC）G $ _2 $歧管以及8维通用连接总和（GCS）旋转（7）歧管的压缩。我们发现，几何结构是通过代数包含钻石在世界表代数中复制的。在论文的第二部分中，我们从超级角度的角度更改齿轮并考虑琴弦压缩。特别是，我们将重点放在杂弦的压缩到三个时空维度上，以保留最小的超对称性$ \ MATHCAL {N} = 1 $，这是由杂种G $ _2 $系统描述的。我们在均质的3-Sasakian流形的带有压缩指标的均质的3 sasakian流形上为该系统建造了广告的新家庭。
In this thesis we study string compactifications on manifolds equipped with a $G$-structure, placing a special emphasis on the interplay between geometry and physics. We follow two complementary approaches. In the first part of the thesis we adopt a sigma model perspective and focus on the worldsheet superconformal field theory. We consider compactifications on 7-dimensional Extra Twisted Connected Sum (ETCS) G$_2$ manifolds as well as 8-dimensional Generalized Connected Sum (GCS) Spin(7) manifolds. We find that the geometric construction is reproduced in the worldsheet algebra via a diamond of algebra inclusions. In the second part of the thesis we change gears and consider string compactifications from a supergravity point of view. In particular, we focus on compactifications of the heterotic string down to three spacetime dimensions preserving minimal supersymmetry $\mathcal{N}=1$, which are described by the heterotic G$_2$ system. We construct new families of AdS$_3$ solutions to this system on homogeneous 3-Sasakian manifolds with squashed metrics.
