## Abstract

We study a *T* ^{2} deformation of large *N* conformal field theories, a higher dimensional generalization of the \( T\overline{T} \) 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 *T* ^{2} deformation.

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Belin, A., Lewkowycz, A. & Sárosi, G. Gravitational path integral from the *T* ^{2} deformation.
*J. High Energ. Phys.* **2020**, 156 (2020). https://doi.org/10.1007/JHEP09(2020)156

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DOI: https://doi.org/10.1007/JHEP09(2020)156