辛Chern-Simons理论与阿贝尔秩$0$理论的对偶
Symplectic Chern-Simons theories dual to Abelian rank-$0$ theories
- Southeast University（东南大学）
- Durham University（杜伦大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出3维辛Chern-Simons理论$USp(2n)$在能级$k=n+\frac12+\ell$时与阿贝尔秩$0$理论$\mathcal{T}_{\ell,n}$对偶，通过匹配超对称真空计数和指标验证，并详细研究$\ell=1$情况。
AI中文摘要：
我们提出，对于每一对正整数$(n,\ell)$，具有一个基本表示中的单个手性多重态的3维辛Chern-Simons理论$USp(2n)$在能级$k=n+\frac12+\ell$处，与Creutzig、Garner和Kim的阿贝尔秩$0$理论$\mathcal{T}_{\ell,n}$对偶。基本表示是伪实的，因此能级是半整数，没有非阿贝尔味对称性，超对称增强为$\mathcal{N}=4$。两侧的Higgs分支和Coulomb分支都消失。我们匹配了所有$(n,\ell)$下实质量形变下的超对称真空计数，并在多种情况下匹配了超对称指标。然后我们详细研究了$\ell=1$的情况，即能级为$n+\frac32$的最小$USp(2n)$ Chern-Simons理论，其对偶是一个具有tadpole能级矩阵和裸磁单极超势的$U(1)^{n}$理论。
英文摘要：
We propose that the 3d symplectic Chern-Simons theory $USp(2n)$ at level $k=n+\frac12+\ell$ with a single chiral multiplet in the fundamental representation is dual, for every pair of positive integers $(n,\ell)$, to the Abelian rank-$0$ theory $\mathcal{T}_{\ell,n}$ of Creutzig, Garner and Kim. The fundamental is pseudo-real, so the level is half-integral, there is no non-Abelian flavor symmetry, and the supersymmetry is enhanced to $\mathcal{N}=4$. Both sides have vanishing Higgs and Coulomb branches. We match the counting of supersymmetric vacua under real mass deformations for all $(n,\ell)$, and the supersymmetric indices in a number of cases. We then study in detail the case $\ell=1$, the minimal $USp(2n)$ Chern-Simons theory at level $n+\frac32$, whose dual is a $U(1)^{n}$ theory with a tadpole level matrix and a bare monopole superpotential.
