标题： $\mathcal{N}=4$超对称杨-米尔斯理论在ADE奇点上的卡西米尔能量的精确简并性与S对偶性 显示英文标题

标题： Exact Degeneracy of Casimir Energy for $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory on ADE Singularities and S-Duality

摘要： 经典上，$\mathcal{N}=4$超对称Yang-Mills理论在$\mathbb{R}\times S^3/\Gamma$上的基态，其中$\Gamma$是$SU(2)$的离散ADE子群，由绕ADE奇点环绕的平坦Wilson线表示。 通过将这些基态与WZW共形块相关联的对偶性，基态简并度不能被量子修正所消除。 使用超共形指标，我们计算了每个平坦Wilson线在不同ADE奇点上的$SU(2)$SYM的超对称卡西米尔能量，并发现所有平坦Wilson线具有相同的超对称卡西米尔能量。 我们认为这种精确的简并度是$\mathcal{N}=4$超对称特有的，并表明当超对称数目减少时，简并度会被消除。 特别是，我们揭示了共形$\mathcal{N}=2$ $SU(2)$ 四味理论在$S^3/\Gamma$上的基态结构的一个令人惊讶的结果。 对于$\mathcal{N}=4$SYM，S-对偶将基态威尔逊线映射到取值于朗兰兹对偶群的基态t'霍夫特线。 我们证明了t'霍夫特线基态的超对称卡西米尔能量与威尔逊线基态相同。 这可以看作是S-对偶性的基态测试。 显示英文摘要

摘要： Classically, the ground states of $\mathcal{N}=4$ supersymmetric Yang-Mills theory on $\mathbb{R}\times S^3/\Gamma$ where $\Gamma$ is a discrete ADE subgroup of $SU(2)$ are represented by flat Wilson lines winding around the ADE singularity. By a duality relating such ground states to WZW conformal blocks, the ground state degeneracy cannot be lifted by quantum corrections. Using the superconformal index, we compute the supersymmetric Casimir energy of each flat Wilson line for $SU(2)$ SYM on different ADE singularities and find that the flat Wilson lines all have the same supersymmetric Casimir energy. We argue that this exact degeneracy is peculiar to $\mathcal{N}=4$ supersymmetry and show that the degeneracy is lifted when the number of supersymmetry is reduced. In particular, we uncover a surprising result for the ground state structure of the conformal $\mathcal{N}=2$ $SU(2)$ four-flavor theory on $S^3/\Gamma$. For $\mathcal{N}=4$ SYM, S-duality maps the ground state Wilson lines to ground state t' Hooft lines taking values in the Langlands dual group. We show that the supersymmetric Casimir energy of the t' Hooft line ground states is the same as the Wilson line ground states. This can be viewed as a ground state test of S-duality.