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Abstract:
We study a T^2 deformation of large N conformal field theories, a higher dimensional generalization of the TTbar 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 a holographic spacetime between two boundaries with Dirichlet boundary conditions for the metric. 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.