# A universal inequality for CFT and quantum gravity

### APA

Hellerman, S. (2009). A universal inequality for CFT and quantum gravity. Perimeter Institute. https://pirsa.org/09070015

### MLA

Hellerman, Simeon. A universal inequality for CFT and quantum gravity. Perimeter Institute, Jul. 02, 2009, https://pirsa.org/09070015

### BibTex

@misc{ pirsa_PIRSA:09070015, doi = {10.48660/09070015}, url = {https://pirsa.org/09070015}, author = {Hellerman, Simeon}, keywords = {Cosmology}, language = {en}, title = {A universal inequality for CFT and quantum gravity}, publisher = {Perimeter Institute}, year = {2009}, month = {jul}, note = {PIRSA:09070015 see, \url{https://pirsa.org}} }

University of Tokyo

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Abstract

The holographic duality gives a one-to-one mapping between consistent theories of gravity with AdS_d ground state, and conformal field theories in d-1 dimensions. Since the latter are unambiguously well-defined, we can use their defining properties to prove rigorous, model-independent theorems covering all quantum gravity theories with negative cosmological constant. Taking d=3, I will prove in this talk that every two-dimensional CFT contains a primary perator of weight less than C /12 + 0.473695, where C is the sum of right- and left-moving central charges. Using the AdS/CFT dictionary, this establishes that every theory of quantum gravity in asymptotically AdS space contains some state of mass less than 1 / (4 G), above and beyond the universal sector of boundary metric excitations.