论文标题
$ t $ - 双溶液和$ g_2 $ -strominger系统的无限模量
$T$-Dual solutions and infinitesimal moduli of the $G_2$-Strominger system
论文作者
论文摘要
我们认为$ g_2 $ - 结构带有扭转的结构，加上$ g_2 $ -instantons，在紧凑型$ 7 $二维的歧管上。耦合是通过方程式以$ 4 $形式出现的，它以超级和广义的几何形状（称为bianchi身份）出现。由弗里德里希（Friedrich）和伊万诺夫（Ivanov）首先研究的部分微分方程系统将杂项字符串的压缩到三个维度，通常称为$ G_2 $ -STROMINGER系统。我们研究溶液的模量空间，并证明无穷小变形的空间，模量自动形态是有限的。我们还为该系统提供了一个新的解决方案家族，以$ t^3 $捆绑$ k3 $表面和无限许多不同的intsanton捆绑包，适应了富考和第二名的作者的构造。特别是，我们展示了该方程式系统的第一个示例。
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.
