论文标题
高能模块化引导程序，全局对称性和缺陷
High Energy Modular Bootstrap, Global Symmetries and Defects
论文作者
论文摘要
我们为在拓扑缺陷线上的不同领域的不同扇区中的运营商增长而得出了类似Cardy的公式，该公式是在拓扑缺陷线上通过在固定$δ$的固定$δ$的情况下将上限和下限放在缩放尺寸的状态下和下限的状态数。因此，我们证明，鉴于有限的全球对称$ g $（忠实地代理），鉴于任何统一的模块化$ 2 $ d cft对称，$ g $的所有不可约的表示都出现在未介绍部门的光谱中；状态的增长与IRREP维度的“正方形”类似，并且成比例。在Schwarzian的极限中，结果与JT重力匹配，具有散装量规理论。如果对称性是非反对的，则结果适用于组元素扭曲的任何扇区。对于$ c> 1 $，对Virasoro初选的陈述是正确的。此外，结果适用于大型CFT。我们还为连续$ u（1）$组扩展了结果。
We derive Cardy-like formulas for the growth of operators in different sectors of unitary $2$ dimensional CFT in the presence of topological defect lines by putting an upper and lower bound on the number of states with scaling dimension in the interval $[Δ-δ,Δ+δ]$ for large $Δ$ at fixed $δ$. Consequently we prove that given any unitary modular invariant $2$D CFT symmetric under finite global symmetry $G$ (acting faithfully), all the irreducible representations of $G$ appear in the spectra of the untwisted sector; the growth of states is Cardy like and proportional to the ''square'' of the dimension of the irrep. In the Schwarzian limit, the result matches onto that of JT gravity with a bulk gauge theory. If the symmetry is non-anomalous, the result applies to any sector twisted by a group element. For $c>1$, the statements are true for Virasoro primaries. Furthermore, the results are applicable to large c CFTs. We also extend our results for the continuous $U(1)$ group.
