Derivation of the GKP-Witten relation by symmetry without Lagrangian
We derive the GKP-Witten relation in terms of correlation functions by symmetry without referring to a Lagrangian or the large N expansion. By constructing bulk operators from boundary operators in conformal field theory (CFT) by the conformal smearing, we first determine bulk-boundary 2-pt function...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-09-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269325005180 |
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| author | Sinya Aoki Janos Balog Kengo Shimada |
| author_facet | Sinya Aoki Janos Balog Kengo Shimada |
| author_sort | Sinya Aoki |
| collection | DOAJ |
| description | We derive the GKP-Witten relation in terms of correlation functions by symmetry without referring to a Lagrangian or the large N expansion. By constructing bulk operators from boundary operators in conformal field theory (CFT) by the conformal smearing, we first determine bulk-boundary 2-pt functions for an arbitrary spin using both conformal and bulk symmetries, then evaluate their small z behaviors, where z is the (d+1)-th coordinate in the bulk. Next, we explicitly determine small z behaviors of bulk-boundary-boundary 3-pt functions also by the symmetries, while small z behaviors of correlation functions among one bulk and n boundary operators with n≥3 are fixed by the operator product expansion (OPE). Combining all results, we construct the GKP-Witten relation in terms of these correlation functions at all orders in an external source J. We compare our non-Lagrangian approach with the standard approach employing the bulk action. Our results indicate that the GKP-Witten relation holds not only for holographic CFTs but also for generic CFTs as long as certain conditions are satisfied. |
| format | Article |
| id | doaj-art-a25e729fe67b4a26a47428733b19a80a |
| institution | Kabale University |
| issn | 0370-2693 |
| language | English |
| publishDate | 2025-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Letters B |
| spelling | doaj-art-a25e729fe67b4a26a47428733b19a80a2025-08-20T03:58:40ZengElsevierPhysics Letters B0370-26932025-09-0186813975710.1016/j.physletb.2025.139757Derivation of the GKP-Witten relation by symmetry without LagrangianSinya Aoki0Janos Balog1Kengo Shimada2Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan; Corresponding author.Holographic QFT Group, Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, H-1525 Budapest 114, P.O.B. 49, HungaryCenter for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, JapanWe derive the GKP-Witten relation in terms of correlation functions by symmetry without referring to a Lagrangian or the large N expansion. By constructing bulk operators from boundary operators in conformal field theory (CFT) by the conformal smearing, we first determine bulk-boundary 2-pt functions for an arbitrary spin using both conformal and bulk symmetries, then evaluate their small z behaviors, where z is the (d+1)-th coordinate in the bulk. Next, we explicitly determine small z behaviors of bulk-boundary-boundary 3-pt functions also by the symmetries, while small z behaviors of correlation functions among one bulk and n boundary operators with n≥3 are fixed by the operator product expansion (OPE). Combining all results, we construct the GKP-Witten relation in terms of these correlation functions at all orders in an external source J. We compare our non-Lagrangian approach with the standard approach employing the bulk action. Our results indicate that the GKP-Witten relation holds not only for holographic CFTs but also for generic CFTs as long as certain conditions are satisfied.http://www.sciencedirect.com/science/article/pii/S0370269325005180 |
| spellingShingle | Sinya Aoki Janos Balog Kengo Shimada Derivation of the GKP-Witten relation by symmetry without Lagrangian Physics Letters B |
| title | Derivation of the GKP-Witten relation by symmetry without Lagrangian |
| title_full | Derivation of the GKP-Witten relation by symmetry without Lagrangian |
| title_fullStr | Derivation of the GKP-Witten relation by symmetry without Lagrangian |
| title_full_unstemmed | Derivation of the GKP-Witten relation by symmetry without Lagrangian |
| title_short | Derivation of the GKP-Witten relation by symmetry without Lagrangian |
| title_sort | derivation of the gkp witten relation by symmetry without lagrangian |
| url | http://www.sciencedirect.com/science/article/pii/S0370269325005180 |
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