সংরক্ষণ করুন:
| প্রধান লেখক: | |
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| বিন্যাস: | Preprint |
| প্রকাশিত: |
2009
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| বিষয়গুলি: | |
| অনলাইন ব্যবহার করুন: | https://arxiv.org/abs/0902.2790 |
| ট্যাগগুলো: |
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| _version_ | 1866915333631115264 |
|---|---|
| author | Hellerman, Simeon |
| author_facet | Hellerman, Simeon |
| contents | We prove that every unitary two-dimensional conformal field theory (with no extended chiral algebra, and with central charges $c_L, c_R > 1$) contains a primary operator with dimension $Δ_1$ that satisfies $0 < Δ_1 < (c_L + c_R)/12 + 0.473695$. Translated into gravitational language using the AdS_3 /CFT_2 dictionary, our result proves rigorously that the lightest massive excitation in any theory of 3D gravity with cosmological constant $Λ< 0$ can be no heavier than $1/(4 G_N) + o(|Λ|^(1/2))$. In the flat-space approximation, this limiting mass is twice that of the lightest BTZ black hole. The derivation of the bound applies at finite central charge for the CFT, and does not rely on an asymptotic expansion at large central charge. Neither does our proof rely on any special property of the CFT such as supersymmetry or holomorphic factorization, nor on any bulk interpretation in terms of string theory or semiclassical gravity. Our only assumptions are unitarity and modular invariance of the dual CFT. Our proof 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0902_2790 |
| institution | arXiv |
| publishDate | 2009 |
| record_format | arxiv |
| spellingShingle | A Universal Inequality for CFT and Quantum Gravity Hellerman, Simeon High Energy Physics - Theory We prove that every unitary two-dimensional conformal field theory (with no extended chiral algebra, and with central charges $c_L, c_R > 1$) contains a primary operator with dimension $Δ_1$ that satisfies $0 < Δ_1 < (c_L + c_R)/12 + 0.473695$. Translated into gravitational language using the AdS_3 /CFT_2 dictionary, our result proves rigorously that the lightest massive excitation in any theory of 3D gravity with cosmological constant $Λ< 0$ can be no heavier than $1/(4 G_N) + o(|Λ|^(1/2))$. In the flat-space approximation, this limiting mass is twice that of the lightest BTZ black hole. The derivation of the bound applies at finite central charge for the CFT, and does not rely on an asymptotic expansion at large central charge. Neither does our proof rely on any special property of the CFT such as supersymmetry or holomorphic factorization, nor on any bulk interpretation in terms of string theory or semiclassical gravity. Our only assumptions are unitarity and modular invariance of the dual CFT. Our proof 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. |
| title | A Universal Inequality for CFT and Quantum Gravity |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/0902.2790 |