论文标题
$ \ MATHCAL {S} $和混合Feigin-Frenkel Gluing的扭曲手性代数
Twisted chiral algebras of class $\mathcal{S}$ and mixed Feigin-Frenkel gluing
论文作者
论文摘要
四维$ \ MATHCAL {N} = 2 $ SUPERCOR-CORM-CORMAL野外理论与顶点操作员代数之间的对应关系，当应用于$ \ Mathcal {S} $的理论时，会导致一个富裕的VOA家族，鉴于Monicker chiral chiral chiral algebras of Class $ \ Mathcal class $ \ Mathcalcalcalcalcalcal {S} $。 Arxiv的Tomoyuki Arakawa提出了这些顶点操作员代数的非常均匀的结构：1811.01577。 Arxiv的构造：1811.01577将简单的lie代数$ \ mathfrak {g} $的选择作为输入，无论$ \ mathfrak {g} $是否简单地适用。然而，在非简单的情况下，所得的VOA并不以任何清晰的方式与已知的四维理论相对应。另一方面，类$ \ Mathcal s $的标准实现涉及非简单的对称代数的代数需要包含外部自动形态扭曲线，这需要进一步发展Arxiv：1811.01577的方法。在本文中，我们介绍了这些进一步的发展，并提出了与外部自动形态扭曲线的$ \ Mathcal S $的大多数手性代数的定义。我们表明我们的定义通过了一些一致性检查，并指出了一些重要的开放问题。
The correspondence between four-dimensional $\mathcal{N}=2$ superconformal field theories and vertex operator algebras, when applied to theories of class $\mathcal{S}$, leads to a rich family of VOAs that have been given the monicker chiral algebras of class $\mathcal{S}$. A remarkably uniform construction of these vertex operator algebras has been put forward by Tomoyuki Arakawa in arXiv:1811.01577. The construction of arXiv:1811.01577 takes as input a choice of simple Lie algebra $\mathfrak{g}$, and applies equally well regardless of whether $\mathfrak{g}$ is simply laced or not. In the non-simply laced case, however, the resulting VOAs do not correspond in any clear way to known four-dimensional theories. On the other hand, the standard realisation of class $\mathcal S$ theories involving non-simply laced symmetry algebras requires the inclusion of outer automorphism twist lines, and this requires a further development of the approach of arXiv:1811.01577. In this paper, we give an account of those further developments and propose definitions of most chiral algebras of class $\mathcal S$ with outer automorphism twist lines. We show that our definition passes some consistency checks and point out some important open problems.
