标题： 瞬子计数在类$\mathcal{S}_k$中 显示英文标题

标题： Instanton counting in Class $\mathcal{S}_k$

摘要： 我们计算了类$\mathcal{S}_k$的$\mathcal{N}=1$超对称共形场论（SCFT）的瞬时子配分函数。 通过orbifold操作Dp/D(p-4)膜系统，并计算位于$K$D(p-4) 膜世界体积上的超对称规范理论的配分函数，得到了这一结果。 Starting with D5/D1 setups probing a $\mathbb{Z}_\ell\times \mathbb{Z}_k$ orbifold singularity we obtain the $K$ instanton partition functions of 6d $(1,0)$ theories on $\mathbb{R}^4 \times T^2$ in the presence of orbifold defects on $T^2$ via computing the 2d superconformal index of the worldvolume theory on $K$ D1 branes wrapping the $T^2$. We then reduce our results to the 5d and to the 4d instanton partition functions. 对于$k=1$，我们验证了是否可以重现已知的椭圆、三角和有理Nekrasov划分函数。 最后，我们证明可以通过施加“ orbifold 条件”$a_{\mathcal{A}} \rightarrow a_A e^{2\pi i j/k}$（包含$\mathcal{A}=jA$和$A=1,\dots, N$,$j=1,\dots, k$）到 Coulomb 模空间和质量参数上来从类$\mathcal{S}$的母理论的瞬子配分函数得到类$\mathcal{S}_k$的$SU(N)$箭图的瞬子配分函数，其中包含$SU(kN)$个规范因子。 显示英文摘要

摘要： We compute the instanton partition functions of $\mathcal{N}=1$ SCFTs in class $\mathcal{S}_k$. We obtain this result via orbifolding Dp/D(p-4) brane systems and calculating the partition function of the supersymmetric gauge theory on the worldvolume of $K$ D(p-4) branes. Starting with D5/D1 setups probing a $\mathbb{Z}_\ell\times \mathbb{Z}_k$ orbifold singularity we obtain the $K$ instanton partition functions of 6d $(1,0)$ theories on $\mathbb{R}^4 \times T^2$ in the presence of orbifold defects on $T^2$ via computing the 2d superconformal index of the worldvolume theory on $K$ D1 branes wrapping the $T^2$. We then reduce our results to the 5d and to the 4d instanton partition functions. For $k=1$ we check that we reproduce the known elliptic, trigonometric and rational Nekrasov partition functions. Finally, we show that the instanton partition functions of $SU(N)$ quivers in class $\mathcal{S}_k$ can be obtained from the class $\mathcal{S}$ mother theory partition functions with $SU(kN)$ gauge factors via imposing the `orbifold condition' $a_{\mathcal{A}} \rightarrow a_A e^{2\pi i j/k}$ with $\mathcal{A}=jA$ and $A=1,\dots, N$, $j=1,\dots, k$ on the Coulomb moduli and the mass parameters.