We study a T2 deformation of large N conformal field theories, a higher dimensional generalization of the TT¯ deformation. The deformed partition function satisfies a flow equation of the diffusion type. We solve this equation by finding its diffusion kernel, which is given by the Euclidean gravitational path integral in d + 1 dimensions between two boundaries with Dirichlet boundary conditions for the metric. This is natural given the connection between the flow equation and the Wheeler-DeWitt equation, on which we offer a new perspective by giving a gauge-invariant relation between the deformed partition function and the radial WDW wave function. An interesting output of the flow equation is the gravitational path integral measure which is consistent with a constrained phase space quantization. Finally, we comment on the relation between the radial wave function and the Hartle-Hawking wave functions dual to states in the CFT, and propose a way of obtaining the volume of the maximal slice from the T2 deformation.
Belin, A., Lewkowycz, A., Sarosi, G. (2020). Gravitational path integral from the T 2 deformation. JOURNAL OF HIGH ENERGY PHYSICS, 2020(9) [10.1007/JHEP09(2020)156].
Gravitational path integral from the T 2 deformation
Belin A
;
2020
Abstract
We study a T2 deformation of large N conformal field theories, a higher dimensional generalization of the TT¯ deformation. The deformed partition function satisfies a flow equation of the diffusion type. We solve this equation by finding its diffusion kernel, which is given by the Euclidean gravitational path integral in d + 1 dimensions between two boundaries with Dirichlet boundary conditions for the metric. This is natural given the connection between the flow equation and the Wheeler-DeWitt equation, on which we offer a new perspective by giving a gauge-invariant relation between the deformed partition function and the radial WDW wave function. An interesting output of the flow equation is the gravitational path integral measure which is consistent with a constrained phase space quantization. Finally, we comment on the relation between the radial wave function and the Hartle-Hawking wave functions dual to states in the CFT, and propose a way of obtaining the volume of the maximal slice from the T2 deformation.File | Dimensione | Formato | |
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