Tauberian-Cardy formula with spin
Tauberian-Cardy formula with spin
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带旋转的陶伯卡迪公式
DOI：
10.1007/jhep01(2020)135
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发表时间：
2019
影响因子：
5.4
通讯作者：
Zheng Sun
中科院分区：
文献类型：
--
作者：
Sridip Pal;Zheng Sun
本文在二维共形场论的背景下证明了一个二维Tauberian定理。利用该定理导出了任意自旋的共形权为（h，h <$ \overline{h} $$）→（∞，∞）的渐近态密度。我们进一步严格地表明，误差项是由扭转参数和不敏感的自旋。讨论了导片对尾旋的敏感性。当平均窗口很大时，我们在微正则熵中确定了一个通用的块。在（h，h <$ \overline{h} $$）平面上存在一个渐近的谱隙，从而导出了渐近的扭转隙.我们证明了一个普遍的不等式，说明在没有任何守恒流的紧致酉二维CFT中Ag ≤ π c − 1 r 2 24 $$ Ag\le \frac{\pi \left（c-1\right）{r}^2}{24} $$满足，其中g是真空上的扭曲间隙，A是最小“面积间隙”，将尺寸上的最小间隙推广到（h ′，h ′ $$ \overline{h}^{\prime } $$）平面和r = 4 3 π <$2.21 $$ r=\frac{4\sqrt{3}}{\pi}\simeq 2.21 $$。我们调查的状态密度的制度，其中自旋参数大于扭曲都走向无穷大。此外，大中心电荷区进行了研究。我们还探讨了态密度的有限扭曲、大自旋行为。
We prove a 2 dimensional Tauberian theorem in context of 2 dimensional conformal field theory. The asymptotic density of states with conformal weight ( h, h ¯ $$ \overline{h} $$ ) → ( ∞, ∞ ) for any arbitrary spin is derived using the theorem. We further rigorously show that the error term is controlled by the twist parameter and insensitive to spin. The sensitivity of the leading piece towards spin is discussed. We identify a universal piece in microcanonical entropy when the averaging window is large. An asymptotic spectral gap on ( h, h ¯ $$ \overline{h} $$ ) plane, hence the asymptotic twist gap is derived. We prove an universal inequality stating that in a compact unitary 2D CFT without any conserved current Ag ≤ π c − 1 r 2 24 $$ Ag\le \frac{\pi \left(c-1\right){r}^2}{24} $$ is satisfied, where g is the twist gap over vacuum and A is the minimal “areal gap”, generalizing the minimal gap in dimension to ( h ′ , h ¯ ′ $$ \overline{h}^{\prime } $$ ) plane and r = 4 3 π ≃ 2.21 $$ r=\frac{4\sqrt{3}}{\pi}\simeq 2.21 $$ . We investigate density of states in the regime where spin is parametrically larger than twist with both going to infinity. Moreover, the large central charge regime is studied. We also probe finite twist, large spin behavior of density of states.