In this talk, I will apply Tauberian technique, a tool from analytic number theory, to analyze the granularity in \textit{averaged} asymptotic data of 2D CFT and learn about the asymptotic spacing of Virasoro primaries. In particular, we show that for a unitary modular invariant 2D CFT with fixed central charge $c>1$, having a nonzero twist gap in the spectrum of Virasoro primaries, for sufficiently large spin $J$, there always exist $\exp\left[2\pi \sqrt{\frac{(c-1) J}{6}}\right]$ number of spin $J$ operators with twist falling in a vanishingly small interval $\left(\frac{c-1}{12} - \varepsilon , \frac{c-1}{12} + \varepsilon \right)$ with $\varepsilon=O(J^{-1/2}\log J)$. A similar result is proven for a family of holographic CFTs with appropriate conditions, in the regime $J>\!\!>c^3>\!\!>1$ having implication on the validity regime of Schwarzian approximation in describing the near-extremal rotating BTZ black holes. I will mention potential extension of the results to CFTs with conserved currents. The talk will mostly be based on $2307.02587$, $2212.04893$ with Jiaxin Qiao and Slava Rychkov and earlier work $2003.14316$, $1905.12636$ with Baur Mukhametzhanov and Shouvik Ganguly.
Zoom link: https://icts-res-in.zoom.us/j/88092766911?pwd=R3ZrVk9yeW96ZmQ4ZG9KRzVhenRKZz09
Meeting ID: 880 9276 6911
Passcode: 232322