Derivation of the GKP-Witten relation by symmetry without Lagrangian
| Autor: | Aoki, Sinya, Balog, Janos, Shimada, Kengo |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $n\ge 3$ 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. Comment: 6 pages, some sentences added to correct errors |
| Databáze: | arXiv |
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