Modular Bootstrap, Elliptic Points, and Quantum Gravity

Abstract

The modular bootstrap program for 2d CFTs could be seen as a systematic exploration of the physical consequences of consistency conditions at the elliptic points and at the cusp of their toruspartition function. The study at $\tau =i$, the elliptic point stabilized by the modular inversion $S$, was initiated by Hellerman, who found a general upper bound for the most relevant scaling dimension $\Delta$. Likewise, analyticity at $\tau =i\infty$, the cusp stabilized by the modular translation $T$, yields an upper bound on the twist gap. Here we study consistency conditions at $\tau =\exp [2i\pi /3]$, the elliptic point stabilized by $ST$. We find a much stronger upper bound in the large-c limit, namely $\Delta <\frac{c-1}{12}+0.092$, which is very close to the minimal mass threshold of the BTZ black holes in the gravity dual of $Ad{S}_3/CF{T}_2$ correspondence.

v4: Eq.(14) corrected. A general proof of the main theorem is described in full details

References in corpus (7)

• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Poincare Series, 3D Gravity and CFT Spectroscopy
• Lightcone Modular Bootstrap and Pure Gravity
• Sphere Packing and Quantum Gravity
• Fast Conformal Bootstrap and Constraints on 3d Gravity
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• Quantum corrections to the BTZ black hole extremality bound from the conformal bootstrap

Cited by in corpus (5)

• Solutions of modular bootstrap constraints from quantum codes
• Quantum stabilizer codes, lattices, and CFTs
• Discreteness and Integrality in Conformal Field Theory
• Fake Z
• Aspects of the S transformation Bootstrap