Exact Renormalization Group for Wave Functionals

Motivated by the construction of continuum tensor networks for interacting field theories, which are relevant in understanding the emergence of space-time in the gauge/gravity correspondence, we derive a non-perturbative functional differential equation for wave functionals in scalar field theories from the exact renormalization group equation. We check the validity of the equation using the perturbation theory. We calculate the wave functional up to the first-order perturbation and verify that it satisfies the equation.