带通量的弦真空与非对易量子场论

We have been working on flux compactification in string theory for the past years. This is closely related to generalized complex geometry..We have made some contributions. In the past years we also found that there is a close relationship between flux compactifications and non-commutative quantum field theory. We propose to further establish the foundations of non-commutative quantum field theory in the.framework of BV formalism and to apply it to contruct string vacua with fluxes. We also work on constructing string vacua with fluxes via F theory.

申请人与课题组多年来致力于研究带通量的弦紧化。这一问题与广义复几何密切相关，我们开展了一些工作并有一定的积累。.近年来我们发现带通量的弦紧化与非对易量子场论也有密切的关系。我们将研究在BV框架下建立非对易量子场论的数学基础.并将其应用于构造带通量的弦真空。我们也致力于用F理论构造带通量的弦真空态。

我们按计划在量子场论的数学构造，带通量的弦真空态的构造上做了一些工作。.量子场论的数学构造是数学物理和理论物理研究的核心课题。我们在时空截断的代数表达，量子反常，范畴化，G2紧化等方面做了些工作。.这也是本项目的核心内容。.1）Feynman geometries，60 Years of Yang-Mills Gauge Field Theories: C.N. Yang's Contributions to Physics, Nanyang Institute of Technology, Singapore..我们提出Feynman几何的概念，用A无穷代数来刻画时空。这个想法用于各种正规化与截断，把各种量子化方案，比如格点场论，弦场论，微扰规范场论，非对易场论等的构造统一起来。这个概念有望成为构造量子场论的基本概念。.2） Geometric aspect of three-dimensional Chern-Simons-like gravity, Journal of Geometry and Physics, 2019, 145: 0-UNSP 103482. SCIE. .3） A Graphical Calculus for Semi-Groupal CategoriesApplied Categorical Structures, 2019, 27(2): 163-197. .4） On geometry of the (generalized) G(2)-manifolds，International Journal of Modern Physics A, Vol. 30, No. 20, 1550112 (2015)..我们还研究了AdS背景下纠缠熵的计算与相变的关系，以及用Yang-Yang函数构造扭结多项式等。