论文标题
渐近界的通用性及其饱和度$ 2 $ d CFT
Universality in asymptotic bounds and its saturation in $2$D CFT
论文作者
论文摘要
我们研究了在统一的，紧凑的$ 2 $ d CFTS中，在重型州的三点系数（轻度轻）和两个相关因子的渐近学研究。我们使用数值辅助的Tauberian技术证明了这种数量上的上限和下限。我们从两个相同标量的OPE中获得了固定旋转的运算符频谱上的最佳上限。尽管所有CFT都遵守了这一界限，但理性的CFT几乎将其饱和。这模仿了状态的渐近密度的范围情景，从而在2D CFT的渐近学中宣布了普遍特征。接下来，我们阐明涂抹在解释与2D CFT中本征态热化有关的渐近结果中的作用。在轻度轻度的三点系数的上下文中，我们发现界限中的一个数字对光运算符与$ \ frac {c} {32} $ threshold的接近程度很敏感。在重度状态下的两个点相关器的背景下，我们发现存在一个神秘的制度，该制度将$ ads_3 $热物理和BTZ黑洞物理学分开。此外，我们为球形保形块的行为提供了一些新的数值结果。
We study asymptotics of three point coefficients (light-light-heavy) and two point correlators in heavy states in unitary, compact $2$D CFTs. We prove an upper and lower bound on such quantities using numerically assisted Tauberian techniques. We obtain an optimal upper bound on the spectrum of operators appearing with fixed spin from the OPE of two identical scalars. While all the CFTs obey this bound, rational CFTs come close to saturating it. This mimics the scenario of bounds on asymptotic density of states and thereby pronounces an universal feature in asymptotics of 2D CFTs. Next, we clarify the role of smearing in interpreting the asymptotic results pertaining to considerations of eigenstate thermalization in 2D CFTs. In the context of light-light-heavy three point coefficients, we find that the order one number in the bound is sensitive to how close the light operators are from the $\frac{c}{32}$ threshold. In context of two point correlator in heavy state, we find the presence of an enigmatic regime which separates the $AdS_3$ thermal physics and the BTZ black hole physics. Furthermore, we present some new numerical results on the behavior of spherical conformal block.
