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arXiv · 2007.00684

Three-dimensional quantum gravity according to ST modular bootstrap

Ferdinando Gliozzi
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Abstract

We combine the large-$c$ ST modular bootstrap equations with the Cardy formula for the asymptotic growth of the density of states to prove that any $2d$ unitary, compact, conformal field theory (CFT) with no higher spin conserved currents leads to conflicting inequalities whenever the entire spectrum of non-trivial primaries lies above the BTZ threshold. As a consequence, the holographic dual of $3d$ pure gravity, if it exists, cannot be a $2d$ CFT. Consistent solutions of ST bootstrap equations require additional primaries lying below the BTZ threshold. The lowest non-trivial primary necessarily has odd spin

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Ferdinando Gliozzi. 2020-07-01. Three-dimensional quantum gravity according to ST modular bootstrap. https://arxiv.org/abs/2007.00684

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