论文标题
$ sl（2，\ mathbb {z}）$在工作中的双重化算法
The $SL(2,\mathbb{Z})$ dualization algorithm at work
论文作者
论文摘要
最近，已经提出了一种将理论二重化为镜子双重双重双重二元组的算法，均以$ 3D $ \ $ \ MATHCAL {n} = 4 $线性颤动以及其$ 4D $ $ $ \ MATHCAL {N} = 1 $ UPLIFT。这模仿了在IIB类型的Brane设置级别进行的操作，该设置工程师$ 3D $理论，其中镜像对称性被认为是$ s $ duality，但它是既定性的，但基于实施$ s $ s $ $ s $ diality的真实侵入性二重奏的应用。在本文中，我们将算法概括为完整的双重组，即$ 3D $中的$ SL（2，\ Mathbb {Z}）$，$ 3D $和$ PSL（2，\ Mathbb {Z}）$ 4D $。这还以$ 3D $ $ \ $ \ MATHCAL {N} = 3 $的二元性产生二元性，其中包括Chern-simons耦合，其中一些增强了$ \ Mathcal {n} = 4 $ supersymmetry，其新的$ 4D $ $ $ $ $ \ $ \ $ \ \ \ \ \ \ \ \ \ \ Mathcal {n} = 1 $ $对方。此外，我们提出了三种方法来研究该算法的最后一步可能出现的VEV触发的RG流动，其中一种使用了实现汉纳尼的新二元性 - 在现场理论中移动。
Recently an algorithm to dualize a theory into its mirror dual has been proposed, both for $3d$ $\mathcal{N}=4$ linear quivers and for their $4d$ $\mathcal{N}=1$ uplift. This mimics the manipulations done at the level of the Type IIB brane setup that engineers the $3d$ theories, where mirror symmetry is realized as $S$-duality, but it is enirely field-theoretic and based on the application of genuine infra-red dualities that implement the local action of $S$-duality on the quiver. In this paper, we generalize the algorithm to the full duality group, which is $SL(2,\mathbb{Z})$ in $3d$ and $PSL(2,\mathbb{Z})$ in $4d$. This also produces dualities for $3d$ $\mathcal{N}=3$ theories with Chern--Simons couplings, some of which have enhanced $\mathcal{N}=4$ supersymmetry, and their new $4d$ $\mathcal{N}=1$ counterpart. In addition, we propose three ways to study the RG flows triggered by possible VEVs appearing at the last step of the algorithm, one of which uses a new duality that implements the Hanany--Witten move in field theory.
