论文标题
表面缺陷，风味模块化微分方程和模块化
Surface defects, flavored modular differential equations and modularity
论文作者
论文摘要
每4D $ \ MATHCAL {N} = 2 $ SCFT $ \ MATHCAL {t} $对应于关联的VOA $ \ MATHBB {V}（\ Mathcal {T}）$，它在通常的非理性中，具有更涉及的代表理论。 $ \ MATHBB {V}中的零状态（\ Mathcal {t}）$可以产生非平凡的调味模块化微分方程，必须通过所有$ \ Mathbb {v}的精制/调味特征来满足（\ Mathcal {t}）$ - 模块。取一些$ a_1 $的理论$ \ mathcal {t} _ {g，n} $ of类 - $ \ mathcal {s} $作为示例，我们构造了Schur索引满足的调味模块化微分方程。我们表明，三种类型的表面缺陷指数为这些微分方程提供了常见的解决方案，因此是$ \ Mathbb {V}（\ Mathcal {t}）$ - 模块字符的来源。这些方程在模块化变换下几乎是协变量的，从而确保存在对数解决方案的存在，这可能与对数模块的特征相对应。
Every 4d $\mathcal{N} = 2$ SCFT $\mathcal{T}$ corresponds to an associated VOA $\mathbb{V}(\mathcal{T})$, which is in general non-rational with a more involved representation theory. Null states in $\mathbb{V}(\mathcal{T})$ can give rise to non-trivial flavored modular differential equations, which must be satisfied by the refined/flavored character of all the $\mathbb{V}(\mathcal{T})$-modules. Taking some $A_1$ theories $\mathcal{T}_{g,n}$ of class-$\mathcal{S}$ as examples, we construct the flavored modular differential equations satisfied by the Schur index. We show that three types of surface defect indices give rise to common solutions to these differential equations, and therefore are sources of $\mathbb{V}(\mathcal{T})$-module characters. These equations transform almost covariantly under modular transformations, ensuring the presence of logarithmic solutions which may correspond to characters of logarithmic modules.
