Three-dimensional quantum gravity according to ST modular bootstrap

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

12 pages, references added and typos corrected

References in corpus (6)

• Three-Dimensional Gravity Revisited
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• JT gravity as a matrix integral
• AdS${}_3$ gravity and random CFT
• Poincare Series, 3D Gravity and CFT Spectroscopy
• Truncatable bootstrap equations in algebraic form and critical surface exponents