Root-$T \overline{T}$ Deformed Boundary Conditions in Holography
| Autor: | Ebert, Stephen, Ferko, Christian, Sun, Zhengdi |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Phys.Rev.D 107 (2023) 12, 126022 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevD.107.126022 |
| Popis: | We develop the holographic dictionary for pure $\mathrm{AdS}_3$ gravity where the Lagrangian of the dual $2d$ conformal field theory has been deformed by an arbitrary function of the energy-momentum tensor. In addition to the $T \overline{T}$ deformation, examples of such functions include a class of marginal stress tensor deformations which are special because they leave the generating functional of connected correlators unchanged up to a redefinition of the source and expectation value. Within this marginal class, we identify the unique deformation that commutes with the $T \overline{T}$ flow, which is the root-$T \overline{T}$ operator, and write down the modified boundary conditions corresponding to this root-$T \overline{T}$ deformation. We also identify the unique marginal stress tensor flow for the cylinder spectrum of the dual CFT which commutes with the inviscid Burgers' flow driven by $T \overline{T}$, and we propose this unique flow as a candidate root-$T \overline{T}$ deformation of the energy levels. We study BTZ black holes in $\mathrm{AdS}_3$ subject to root-$T \overline{T}$ deformed boundary conditions, and find that their masses flow in a way which is identical to that of our candidate root-$T \overline{T}$ energy flow equation, which offers evidence that this flow is the correct one. Finally, we also obtain the root-$T \overline{T}$ deformed boundary conditions for the gauge field in the Chern-Simons formulation of $\mathrm{AdS}_3$ gravity. Comment: 65 pages, LaTeX; v2: typos corrected and references added; v3: published version |
| Databáze: | arXiv |
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