Generalising G2 geometry: involutivity, moment maps and moduli
Generalising G2 geometry: involutivity, moment maps and moduli
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G2几何的推广：对合性、矩映射和模
DOI：
10.1007/jhep01(2021)158
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发表时间：
2019-10
影响因子：
5.4
通讯作者：
A. Ashmore;C. Strickland‐Constable;David Tennyson;D. Waldram
中科院分区：
文献类型：
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作者：
A. Ashmore;C. Strickland‐Constable;David Tennyson;D. Waldram
我们分析了弦理论中一般的Minkowski=1，D=4磁通紧致的几何，这是建立弦模型的默认背景。在M-理论中，它们是G2完整流形的自然弦理论推广。在第二类理论中，它们扩展了Calabi-Yau几何的概念，并包括了基于Graña等人(GMPT)最先考虑的广义复杂结构的通量背景类。利用E7(7)×ℝ+广义几何，我们证明了这些紧化是由定义广义切空间的对合子丛的SU(7)⊂E7(7)结构和与理论的微分同胚和规范对称作用相对应的消失矩映射来刻画的。结构空间上的Kähler势定义了Hitchin的G2泛函的自然推广.利用这个框架，我们第一次能够用广义几何上同调群来计算GMPT解的无质量标量模。它还为G2流形的存在提供了一个有趣的新视角，表明它可能与几何不变理论和稳定性有关。
We analyse the geometry of generic Minkowski= 1, D= 4 flux compactifications in string theory, the default backgrounds for string model building. In M-theory they are the natural string theoretic extensions of G2 holonomy manifolds. In type II theories, they extend the notion of Calabi-Yau geometry and include the class of flux backgrounds based on generalised complex structures first considered by Graña et al.(GMPT). Using E 7 (7)× ℝ+ generalised geometry we show that these compactifications are characterised by an SU (7)⊂ E 7 (7) structure defining an involutive subbundle of the generalised tangent space, and with a vanishing moment map, corresponding to the action of the diffeomorphism and gauge symmetries of the theory. The Kähler potential on the space of structures defines a natural extension of Hitchin’s G 2 functional. Using this framework we are able to count, for the first time, the massless scalar moduli of GMPT solutions in terms of generalised geometry cohomology groups. It also provides an intriguing new perspective on the existence of G 2 manifolds, suggesting possible connections to Geometrical Invariant Theory and stability.