标题： 关于离散群orbifold的duality缺陷在$c=2$紧致玻色CFT中的分类 显示英文标题

标题： On the classification of duality defects in $c=2$ compact boson CFTs with a discrete group orbifold

摘要： 我们提出了一种探索紧致玻色子共形场论（CFT）中对偶缺陷的新方法，记为 $c=2$。 这项研究的动机来源于对分类 CFT 中的范畴对称性，特别是对偶缺陷的兴趣。 虽然 $c=1$ 的情况已经被广泛研究，并且可实现的对偶缺陷类型大多已被理解，但对于 $c=2$ 的情况，情形变得更加复杂。 $c=1$ 的简单性源于其理论本质上由紧致化半径决定。 相比之下，$c=2$ 涉及更多参数，导致 T 对偶作用更加复杂。 因此，直接求解理论在 orbifolding 下自对偶的条件变得非常具有挑战性。 为了解决这个问题，我们将对偶缺陷分为四类，并证明了在由平移对称生成的自同构诱导的 orbifolding 下，环面分支理论自对偶的条件可以重新表述为二次方程。 我们还发现，对于“几乎所有”理论，我们可以枚举出这些方程的所有解。 此外，这种重新表述使得同时探索多个对偶缺陷成为可能，并为特定参数族下的理论存在对偶缺陷提供了证据，例如在 $(\tau, \rho) = (it, \frac{1}{2}+it)$ 中当 $t \in \mathbb{Q}$。 显示英文摘要

摘要： We propose a novel approach to exploring duality defects in the $c=2$ compact boson conformal field theory (CFT). This study is motivated by the desire to classify categorical symmetries, particularly duality defects, in CFTs. While the $c=1$ case has been extensively studied, and the types of realizable duality defects are largely understood, the situation becomes significantly more complex for $c=2$. The simplicity of the $c=1$ case arises from the fact that its theory is essentially determined by the radius of compactification. In contrast, the $c=2$ case involves more parameters, leading to a more intricate action of T-duality. As a result, directly solving the condition for a theory to be self-dual under orbifolding becomes highly challenging. To address this, we categorize duality defects into four types and demonstrate that the condition for a toroidal branch theory to be self-dual under an orbifold induced by an automorphism generated by shift symmetry can be reformulated as quadratic equations. We also found that for ``almost all" theories we can enumerate all solutions for such equations. Moreover, this reformulation enables the simultaneous exploration of multiple duality defects and provides evidence for the existence of duality defects under specific parameter families for the theory, such as $(\tau, \rho) = (it, \frac{1}{2}+it)$ where $t \in \mathbb{Q}$.