论文标题
镜头空间上的符号量规组
Symplectic gauge group on the Lens Space
论文作者
论文摘要
我们计算4D超对称仪表理论的镜头空间指数涉及符号量规组。该指数可以区分给定代数的不同仪表组与超对称二元性相关的理论匹配。我们为$ \ Mathcal {n} = 4 $ SYM提供明确的计算，以及$ \ Mathcal {n} = 2 $和$ \ Mathcal {n} = 1 $ lagrangian Quivers的类别。在这些情况下，索引在s偶阶段匹配，而不同S-偶性轨道的模型则具有不同的镜头索引。我们为4D $ \ MATHCAL {n} = 1 $ toric Quiver仪表理论提供类似的计算，该理论对应于$ \ Mathbb {z} _7 $ orbifold $ \ Mathbb {C {C}^3 $。在$ n = 2 $的情况下，这种$ su（n）^7 $量学理论变得有趣，因为它是其他两个模型的偶性，具有符号和统一的量规组，双烟素和反对称张量。我们在镜头空间指数级别上明确检查此试验。
We compute the Lens space index for 4d supersymmetric gauge theories involving symplectic gauge groups. This index can distinguish between different gauge groups from a given algebra and it matches across theories related by supersymmetric dualities. We provide explicit calculations for $\mathcal{N}=4$ SYM and for classes of $\mathcal{N}=2$ and $\mathcal{N}=1$ Lagrangian quivers related by S-duality. In these cases the index matches across the S-dual phases, while models in different S-duality orbits have a different Lens index. We provide analogous computations for a 4d $\mathcal{N}=1$ toric quiver gauge theory corresponding to a $\mathbb{Z}_7$ orbifold of $\mathbb{C}^3$. This $SU(n)^7$ gauge theory becomes interesting in the case of $n=2$ because it is conformally dual to other two models, with symplectic and unitary gauge groups, bifundamentals and antisymmetric tensors. We explicitly check this triality at the level of the Lens space index.
