Universal bounds on CFT Distance Conjecture
Abstract For any unitary conformal field theory in two dimensions with the central charge c, we prove that, if there is a nontrivial primary operator whose conformal dimension ∆ vanishes in some limit on the conformal manifold, the Zamolodchikov distance t to the limit is infinite, the approach to t...
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2024-12-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP12(2024)154 |
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| author | Hirosi Ooguri Yifan Wang |
| author_facet | Hirosi Ooguri Yifan Wang |
| author_sort | Hirosi Ooguri |
| collection | DOAJ |
| description | Abstract For any unitary conformal field theory in two dimensions with the central charge c, we prove that, if there is a nontrivial primary operator whose conformal dimension ∆ vanishes in some limit on the conformal manifold, the Zamolodchikov distance t to the limit is infinite, the approach to this limit is exponential ∆ = exp(−αt + O(1)), and the decay rate obeys the universal bounds c −1/2 ≤ α ≤ 1. In the limit, we also find that an infinite tower of primary operators emerges without a gap above the vacuum and that the conformal field theory becomes locally a tensor product of a sigma-model in the large radius limit and a compact theory. As a corollary, we establish a part of the Distance Conjecture about gravitational theories in three-dimensional anti-de Sitter space. In particular, our bounds on α indicate that the emergence of exponentially light states is inevitable as the moduli field corresponding to t rolls beyond the Planck scale along the steepest path and that this phenomenon can begin already at the curvature scale of the bulk geometry. We also comment on implications of our bounds for gravity in asymptotically flat spacetime by taking the flat space limit and compare with the Sharpened Distance Conjecture. |
| format | Article |
| id | doaj-art-43d55f1dea1e4c6e91cfe2df4e4c1c67 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | SpringerOpen |
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| series | Journal of High Energy Physics |
| spelling | doaj-art-43d55f1dea1e4c6e91cfe2df4e4c1c672025-01-05T12:06:41ZengSpringerOpenJournal of High Energy Physics1029-84792024-12-0120241213610.1007/JHEP12(2024)154Universal bounds on CFT Distance ConjectureHirosi Ooguri0Yifan Wang1Walter Burke Institute for Theoretical Physics, California Institute of TechnologyCenter for Cosmology and Particle Physics, New York UniversityAbstract For any unitary conformal field theory in two dimensions with the central charge c, we prove that, if there is a nontrivial primary operator whose conformal dimension ∆ vanishes in some limit on the conformal manifold, the Zamolodchikov distance t to the limit is infinite, the approach to this limit is exponential ∆ = exp(−αt + O(1)), and the decay rate obeys the universal bounds c −1/2 ≤ α ≤ 1. In the limit, we also find that an infinite tower of primary operators emerges without a gap above the vacuum and that the conformal field theory becomes locally a tensor product of a sigma-model in the large radius limit and a compact theory. As a corollary, we establish a part of the Distance Conjecture about gravitational theories in three-dimensional anti-de Sitter space. In particular, our bounds on α indicate that the emergence of exponentially light states is inevitable as the moduli field corresponding to t rolls beyond the Planck scale along the steepest path and that this phenomenon can begin already at the curvature scale of the bulk geometry. We also comment on implications of our bounds for gravity in asymptotically flat spacetime by taking the flat space limit and compare with the Sharpened Distance Conjecture.https://doi.org/10.1007/JHEP12(2024)154AdS-CFT CorrespondenceConformal Field Models in String TheoryScale and Conformal Symmetries |
| spellingShingle | Hirosi Ooguri Yifan Wang Universal bounds on CFT Distance Conjecture Journal of High Energy Physics AdS-CFT Correspondence Conformal Field Models in String Theory Scale and Conformal Symmetries |
| title | Universal bounds on CFT Distance Conjecture |
| title_full | Universal bounds on CFT Distance Conjecture |
| title_fullStr | Universal bounds on CFT Distance Conjecture |
| title_full_unstemmed | Universal bounds on CFT Distance Conjecture |
| title_short | Universal bounds on CFT Distance Conjecture |
| title_sort | universal bounds on cft distance conjecture |
| topic | AdS-CFT Correspondence Conformal Field Models in String Theory Scale and Conformal Symmetries |
| url | https://doi.org/10.1007/JHEP12(2024)154 |
| work_keys_str_mv | AT hirosiooguri universalboundsoncftdistanceconjecture AT yifanwang universalboundsoncftdistanceconjecture |