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We propose a method for the (re)-construction of a regularized functionalintegral, well defined in the ultraviolet limit, from a solution of thefunctional renormalization group equation of the effective average action. Thefunctional integral is required to reproduce this solution. The method is ofparticular interest for asymptotically safe theories. The bare action for theEinstein-Hilbert truncation of Quantum Einstein Gravity (QEG) is computed andits flow is analyzed. As a second example conformally reduced gravity isexplored. Various conceptual issues related to the reconstruction problem arediscussed.

Bare vs. Effective Fixed Point Action in Asymptotic Safety: The Reconstruction Problem