标题： 旋量-矢量对偶性与镜像对称性 显示英文标题

标题： Spinor-Vector Duality and Mirror Symmetry

摘要： 镜像对称性最初在世界面弦构造中被观察到，并被证明在弦紧化有效场论（EFT）极限中具有深远的意义，以及在卡拉比-丘流形的性质中。 它开启了一个纯数学的新领域，并被应用于枚举几何领域。 旋量-矢量对偶性（SVD）是镜像对称性的扩展。 这可以通过异位弦的环面紧化模空间来直观理解，这些模空间包括度规、反对称张量场和威尔逊线模空间。 就环面模空间而言，镜像对称性对应于内部空间模空间的映射，而旋量-矢量对偶性则对应于威尔逊线模空间的映射。 在过去几年中，我们证明了弦理论有效场论紧化中旋量-矢量对偶性的存在。 这是通过从一个表现出旋量-矢量对偶性的世界面轨道构造开始，并解决轨道奇点，从而生成一个带有旋量-矢量对偶性印记的平滑有效场论极限来实现的。 就像镜像对称性一样，旋量-矢量对偶性可以用来研究带有向量丛的复流形的性质。 旋量-矢量对偶性通过探索紫外完备的世界面弦构造的对称性在有效场论极限中的印记，为“荒野”计划提供了一种自上而下的方法。 SVD表明了具有紫外完备嵌入的(2,0) EFT与不具有紫外完备嵌入的EFT之间的分界线。 显示英文摘要

摘要： Mirror symmetry was first observed in worldsheet string constructions and shown to have profound implications in the Effective Field Theory (EFT) limit of string compactifications, and for the properties of Calabi-Yau manifolds. It opened up a new field in pure mathematics and was utilised in the area of enumerative geometry. Spinor-Vector Duality (SVD) is an extension of mirror symmetry. This can be readily understood in terms of the moduli of toroidal compactification of the heterotic string, which include the metric the antisymmetric tensor field and the Wilson line moduli. In terms of toroidal moduli, mirror symmetry corresponds to mappings of the internal space moduli, whereas spinor-vector duality corresponds to maps of the Wilson line moduli. In the past few of years, we demonstrated the existence of spinor-vector duality in the effective field theory compactifications of the string theories. This was achieved by starting with a worldsheet orbifold construction that exhibited spinor-vector duality and resolving the orbifold singularities, hence generating a smooth effective field theory limit with an imprint of the spinor-vector duality. Just like mirror symmetry, the spinor-vector duality can be used to study the properties of complex manifolds with vector bundles. Spinor--vector duality offers a top-down approach to the ``Swampland''-program, by exploring the imprint of the symmetries of the ultra-violet complete worldsheet string constructions in the effective field theory limit. The SVD suggests a demarcation line between (2,0) EFTs that possess an ultra-violet complete embedding versus those that do not.