Geometric flows for the Type IIA string

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2020-11-07 DOI:10.4310/cjm.2021.v9.n3.a3

Teng Fei, D. Phong, Sebastien Picard, Xiangwen Zhang

引用次数: 18

Abstract

A geometric flow on $6$-dimensional symplectic manifolds is introduced which is motivated by supersymmetric compactifications of the Type IIA string. The underlying structure turns out to be SU(3) holonomy, but with respect to the projected Levi-Civita connection of an almost-Hermitian structure. The short-time existence is established, and new identities for the Nijenhuis tensor are found which are crucial for Shi-type estimates. The integrable case can be completely solved, giving an alternative proof of Yau's theorem on Ricci-flat K\"ahler metrics. In the non-integrable case, models are worked out which suggest that the flow should lead to optimal almost-complex structures compatible with the given symplectic form.

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IIA型管柱的几何流量

在IIA型弦的超对称紧化的基础上，引入了$6$维辛流形上的一个几何流。基础结构原来是SU（3）holonomy，但关于几乎埃尔米特结构的投影Levi-Civita连接。建立了短时存在性，并发现了Nijenhuis张量的新恒等式，这对Shi型估计至关重要。可积情况可以完全求解，给出了Ricci平坦K\“ahler度量上的Yau定理的另一个证明。在不可积情况下，建立了模型，表明流应该导致与给定辛形式兼容的最优几乎复杂结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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