标题： 有理RG流，扩展和Witt类 显示英文标题

标题： Rational RG flow, extension, and Witt class

摘要： 考虑一个保持预模融合范畴$\mathcal S_1$的重整化群流。 如果它流向一个有理共形场理论，残留的对称性$\mathcal S_1$流向一个具有张量函子$F:\mathcal S_1\to\mathcal S_2$的预模融合范畴$\mathcal S_2$。 通过澄清重整化群域墙/界面或边界条件的数学（尤其是范畴论）意义，我们发现隐藏的扩展顶点算子（超）代数给出了Witt等价类$[\mathcal S_1\boxtimes\mathcal S_2]$的唯一（至辫子等价）完全$(\mathcal S_1\boxtimes\mathcal S_2)'$-各向异性代表。 这个数学猜想在物理上得到了支持，并在具体的例子中通过了各种测试，包括非单位最小模型和Wess-Zumino-Witten模型。 特别是，该猜想超越了对角余集。 这一图景还确立了假设的半整数条件，该条件确定了红外共形维度模$\frac12$。 它进一步导致了双辫子关系，即辫子结构在共形固定点处跳跃。 作为应用，我们求解了来自$E$型极小模型的$(A_{10},E_6)\to M(4,3)$流。 显示英文摘要

摘要： Consider a renormalization group flow preserving a pre-modular fusion category $\mathcal S_1$. If it flows to a rational conformal field theory, the surviving symmetry $\mathcal S_1$ flows to a pre-modular fusion category $\mathcal S_2$ with monoidal functor $F:\mathcal S_1\to\mathcal S_2$. By clarifying mathematical (especially category theoretical) meaning of renormalization group domain wall/interface or boundary condition, we find the hidden extended vertex operator (super)algebra gives a unique (up to braided equivalence) completely $(\mathcal S_1\boxtimes\mathcal S_2)'$-anisotropic representative of the Witt equivalence class $[\mathcal S_1\boxtimes\mathcal S_2]$. The mathematical conjecture is supported physically, and passes various tests in concrete examples including non/unitary minimal models, and Wess-Zumino-Witten models. In particular, the conjecture holds beyond diagonal cosets. The picture also establishes the conjectured half-integer condition, which fixes infrared conformal dimensions mod $\frac12$. It further leads to the double braiding relation, namely braiding structures jump at conformal fixed points. As an application, we solve the flow from the $E$-type minimal model $(A_{10},E_6)\to M(4,3)$.