The Strong Gravity Theorem: a model-independent inequality in quantum gravity

          @misc{ pirsa_PIRSA:09010040,
            doi = {10.48660/09010040},
            url = {https://pirsa.org/09010040},
            author = {Hellerman, Simeon},
            keywords = {Quantum Gravity, Quantum Fields and Strings},
            language = {en},
            title = {The Strong Gravity Theorem: a model-independent inequality in quantum gravity},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {jan},
            note = {PIRSA:09010040 see, \url{https://pirsa.org}}
          }
          

Abstract

We derive a universal upper bound on the weight of the lowest primary operator in any two-dimensional conformal field theory with a given central charge. Translated into gravitational language using the AdS/CFT dictionary, our result proves rigorously that the lightest massive state in any theory of 3D gravity and matter with negative cosmological constant can be no heavier than a particular function the cosmological constant and the Planck scale. For a large AdS space, the lower bound approaches the mass of the lightest BTZ black hole. The derivation applies at finite central charge and does not rely on an asymptotic expansion at large central charge, or on any use of semiclassical or bulk physics. Neither does our proof rely on any special property of the CFT such as supersymmetry or holomorphic factorization. The only assumptions are unitarity, modular invariance, and a discrete spectrum. Our proof firmly demonstrates for the first time that there exists a universal center-of-mass energy beyond which a theory of 'pure' quantum gravity can never consistently be extended.