论文标题
属属的手性代数$ \ mathcal {s} $理论
The Chiral Algebra of Genus Two Class $\mathcal{S}$ Theory
论文作者
论文摘要
我们构建与$ a_ {1} $相关的手性代数 - 类型类别$ \ mathcal {s} $理论，用于两个无刺的riemann表面。通过解决与四个维度的边缘测量相对应的BRST共同学问题，我们发现形成封闭操作的一组手性代数发生器。鉴于他们将手性代数操作员的频谱重现至大尺寸，因此我们认为它们是一组完整的发电机集。值得注意的是，他们的操作是在$ su（2）$的动作下是不变的，这与四个维度的任何保守的一式电流无关。我们发现，这种新颖的$ su（2）$在很大程度上限制了非量表Schur运营商的选择。为了完整性，我们还检查了在两个S二维描述中计算出的Schur指数的等效性，并打开了非散布风味的散发性。
We construct the chiral algebra associated with the $A_{1}$-type class $\mathcal{S}$ theory for genus two Riemann surface without punctures. By solving the BRST cohomology problem corresponding to a marginal gauging in four dimensions, we find a set of chiral algebra generators that form closed OPEs. Given the fact that they reproduce the spectrum of chiral algebra operators up to large dimensions, we conjecture that they are the complete set of generators. Remarkably, their OPEs are invariant under an action of $SU(2)$ which is not associated with any conserved one-form current in four dimensions. We find that this novel $SU(2)$ strongly constrains the OPEs of non-scalar Schur operators. For completeness, we also check the equivalence of Schur indices computed in two S-dual descriptions with a non-vanishing flavor fugacity turned on.
