Mixed boundary conditions and Double-trace like deformations in Celestial holography and Wedge-like holography

• URL: http://arxiv.org/abs/2305.10779v3
• Date: Fri, 26 Apr 2024 11:06:51 GMT
• Title: Mixed boundary conditions and Double-trace like deformations in Celestial holography and Wedge-like holography
• Authors: Machiko Fukada, Akihiro Miyata,
• Abstract summary: We consider deformations of boundary conditions in flat spacetimes under flat space co-dimension-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. In the latter Wedge-like holography, we consider mixed Neumann/Dirichlet boundary conditions on the null infinity of the light-cone.
• Score: 1.688134675717698
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: According to the AdS/CFT dictionary, adding a relevant double-trace deformation $f\int O^2$ 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 co-dimension-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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