SM&FT 2019 - The XVIII Workshop on Statistical Mechanics and nonpertubative Field Theory

Forgotten modular bootstrap equations and 3d quantum gravity

13 Dec 2019, 09:30

15m

Salone degli Affreschi, Palazzo Ateneo Università "Aldo Moro" Bari

Session 9

Speaker

Ferdinando Gliozzi (INFN, Sezione di Torino)

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 ${\mathrm{\Delta }}_0$. Likewise, analyticity at $\tau =i\mathrm{\infty }$, 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 $ST$ 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 ${\mathrm{\Delta }}_0$ down this threshold, implying that
pure Einstein gravity do not exist as a quantum theory.

Presentation materials

bari19.pdf