$G_2$-Strominger系统的$T$-对偶解和无穷小模

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Advances in Theoretical and Mathematical Physics Pub Date : 2020-05-20 DOI:10.4310/atmp.2022.v26.n6.a3
Andrew Clarke, M. Garcia‐Fernandez, C. Tipler
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引用次数: 10

摘要

在一个紧凑的$7维流形上,考虑$G_2$-结构与$G_2$-实例耦合的问题。这种耦合是通过一个$4$-形式的方程实现的,它出现在超重力和广义几何中,被称为Bianchi恒等式。首先由Friedrich和Ivanov研究,得到的偏微分方程组描述了异质弦在三维空间的紧化,通常被称为G_2 -Strominger系统。研究了解的模空间,证明了模自同构的无穷小变形空间是有限维的。采用Fu-Yau和第二作者的构造,在$K3$表面上的$T^3$-束和无穷多个不同的瞬时束上,给出了该系统的一个新的解族。特别地,我们展示了这个方程组的$T$对偶解的第一个例子。
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$T$-dual solutions and infinitesimal moduli of the $G_2$-Strominger system
We consider $G_2$-structures with torsion coupled with $G_2$-instantons, on a compact $7$-dimensional manifold. The coupling is via an equation for $4$-forms which appears in supergravity and generalized geometry, known as the Bianchi identity. First studied by Friedrich and Ivanov, the resulting system of partial differential equations describes compactifications of the heterotic string to three dimensions, and is often referred to as the $G_2$-Strominger system. We study the moduli space of solutions and prove that the space of infinitesimal deformations, modulo automorphisms, is finite dimensional. We also provide a new family of solutions to this system, on $T^3$-bundles over $K3$ surfaces and for infinitely many different instanton bundles, adapting a construction of Fu-Yau and the second named author. In particular, we exhibit the first examples of $T$-dual solutions for this system of equations.
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来源期刊
Advances in Theoretical and Mathematical Physics
Advances in Theoretical and Mathematical Physics 物理-物理:粒子与场物理
CiteScore
2.20
自引率
6.70%
发文量
0
审稿时长
>12 weeks
期刊介绍: Advances in Theoretical and Mathematical Physics is a bimonthly publication of the International Press, publishing papers on all areas in which theoretical physics and mathematics interact with each other.
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