论文标题
扭曲的超级重力和Koszul二元性：ADS中的案例研究$ _3 $
Twisted Supergravity and Koszul Duality: A case study in AdS$_3$
论文作者
论文摘要
在本说明中，我们研究了ADS上的超级重力$ _3 \ times S^3 \ times t^4 $与Scft（在对称的Orbifold理论$ sym^n（t^4）$ as $ n \ rightarrow \ rightarrow \ iffty $之间的简化变体。这种变体是由第一作者和si li提出的转折产生的。我们恢复了有关直接在扭曲散装理论中工作的原始双重性的受保护子截面的许多结果。此外，我们确定在扭曲引力理论的$ n \ rightarrow \ infty $限制中产生的对称代数。我们强调了$ \ textit {koszul duality} $ ---在字段理论和弦理论中提供友好介绍的无处不在数学概念。在说明了Holomorphic Chern-Simons理论的“玩具”示例中Koszul二元性的出现之后，我们描述了Koszul二元性的（变形）如何将散装和边界运算符在我们扭曲的设置中，并解释一个人如何使用此概念来计算代数。进一步的细节，结果和计算将出现在同伴论文中。
In this note, we study a simplified variant of the familiar holographic duality between supergravity on AdS$_3\times S^3\times T^4$ and the SCFT (on the moduli space of) the symmetric orbifold theory $Sym^N(T^4)$ as $N \rightarrow \infty$. This variant arises conjecturally from a twist proposed by the first author and Si Li. We recover a number of results concerning protected subsectors of the original duality working directly in the twisted bulk theory. Moreover, we identify the symmetry algebra arising in the $N\rightarrow \infty$ limit of the twisted gravitational theory. We emphasize the role of $\textit{Koszul duality}$---a ubiquitous mathematical notion to which we provide a friendly introduction---in field theory and string theory. After illustrating the appearance of Koszul duality in the "toy" example of holomorphic Chern-Simons theory, we describe how (a deformation of) Koszul duality relates bulk and boundary operators in our twisted setup, and explain how one can compute algebra OPEs diagrammatically using this notion. Further details, results, and computations will appear in a companion paper.
