Speaker
Description
The modular bootstrap program for two-dimensional conformal field theories could be seen as a systematic exploration of the physical consequences of consistency conditions at the elliptic points and at the cusp of their torus partition function. The study at $\tau=i$, the elliptic point stabilized by the modular inversion $S$, was initiated in 2009 by Hellerman, who found a general upper bound for the most relevant scaling dimension $\Delta_0$. Likewise, analyticity at $\tau=i\infty$, the cusp stabilized by the modular translation $T$, yields an upper bound on the twist gap, whereas to date
the study at $\tau=\exp[2i\pi/3]$, the elliptic point stabilized by $S\,T$ has been neglected.
Here I found a far stronger upper bound in the large-$c$ limit which is remarkably close to
the minimal mass threshold of the BTZ black holes in the holographic dual $3d$ gravity. Even a modest improvement could push $\Delta_0$ down this threshold, implying that
pure Einstein gravity do not exist as a quantum theory.
