Abstract
According to the AdS/CFT dictionary, adding a relevant double-trace deformation f ∫ O2 to a holographic CFT action is dual to imposing mixed Neumann/Dirichlet boundary conditions for the field dual to O in AdS. We observed similar behaviour in codimension-two flat space holographies. We consider deformations of boundary conditions in flat spacetimes under flat space codimension-two holographies, Celestial holography and Wedge-like holography. In the former Celestial-holographic approach, we imposed boundary conditions on initial and final bulk states in the scattering. We find that these non-trivial boundary conditions in the bulk induce “double deformations” on the Celestial CFT side, which can be understood as an analogy of double trace deformations in the usual AdS/CFT. We compute two-point bulk scattering amplitudes under the non-trivial deformed boundary conditions. In the latter Wedge-like holography approach, we consider mixed Neumann/Dirichlet boundary conditions on the null infinity of the light-cone. We find that this mixing induces a renormalization flow in the dual Wedge CFT side under the Wedge holography, as in the usual AdS/CFT. We argue that the discrepancy between the Wedge two-point function and the Celestial two-point function originates from a sensitivity of bulk massless fields to a regularization parameter to use the usual AdS/CFT techniques.
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Acknowledgments
We thank Yoshio Kikukawa for useful discussions in the early stage of this project and for useful comments on the draft. MF thanks Sotaro Sugishita, Hayato Hirai for useful discussions in the related projects. MF also thanks to Hoiki Liu for correspondence. AM thanks Yuki Matsumoto for useful discussions in the related projects. AM also thanks Tadashi Takayanagi for correspondence.
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Fukada, M., Miyata, A. Mixed boundary conditions and double-trace like deformations in Celestial holography and Wedge-like holography. J. High Energ. Phys. 2024, 88 (2024). https://doi.org/10.1007/JHEP04(2024)088
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DOI: https://doi.org/10.1007/JHEP04(2024)088