Bethe/Gauge对应的等变U（N）Verlinde代数
Equivariant U(N) Verlinde algebra from Bethe/Gauge correspondence
摘要：
本文计算了$Σ_g \times S^1$上带有伴随手征多重态的$\mathcal{N}=2$ $U(N)$ Chern-Simons理论的拓扑配分函数（扭曲指数）。局部化技术表明，其基础Frobenius代数是等变Verlinde代数，该代数是由$U(1)$等变参数$t$正则化的复Chern-Simons理论的正则量子化得到的.我们的计算依赖于一个贝特/规范对应，使我们能够代表的Hall-Littlewood多项式$P_λ(x_B, t)$与贝特根$x_B$的$q$玻色子模型的专业化方面的等变Verlinde代数。我们证实了一个建议的对偶性的库仑分支极限的透镜空间超共形指数的四维$\mathcal{N}=2$理论的$SU(2)$和$SU(3)$与较低的水平。在$SU(2)$情形中，我们还提出了基于Jeffrey-Kirwan剩余运算的更直接的计算方法。
英文摘要：
We compute the topological partition function (twisted index) of $\mathcal{N}=2$ $U(N)$ Chern-Simons theory with an adjoint chiral multiplet on $Σ_g \times S^1$. The localization technique shows that the underlying Frobenius algebra is the equivariant Verlinde algebra which is obtained from the canonical quantization of the complex Chern-Simons theory regularized by $U(1)$ equivariant parameter $t$. Our computation relies on a Bethe/Gauge correspondence which allows us to represent the equivariant Verlinde algebra in terms of the Hall-Littlewood polynomials $P_λ(x_B, t)$ with a specialization by Bethe roots $x_B$ of the $q$-boson model. We confirm a proposed duality to the Coulomb branch limit of the lens space superconformal index of four dimensional $\mathcal{N}=2$ theories for $SU(2)$ and $SU(3)$ with lower levels. In $SU(2)$ case we also present more direct computation based on Jeffrey-Kirwan residue operation.
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