Modular Bootstrap, Elliptic Points, and Quantum Gravity
arXiv:1908.00029 · doi:10.1103/PhysRevResearch.2.013327
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 , the elliptic point stabilized by the modular inversion , was initiated by Hellerman, who found a general upper bound for the most relevant scaling dimension . Likewise, analyticity at , the cusp stabilized by the modular translation , yields an upper bound on the twist gap. Here we study consistency conditions at , the elliptic point stabilized by . We find a much stronger upper bound in the large-c limit, namely , which is very close to the minimal mass threshold of the BTZ black holes in the gravity dual of correspondence.
arXiv commentv4: Eq.(14) corrected. A general proof of the main theorem is described in full details
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