## Details

I will discuss log corrections to the gravitational path integral around asymptotically Euclidean AdS4 backgrounds that arise from the compactification of string/M-theory. The heat kernel method will be utilized, which divides the log correction into local and non-local contributions. The local contribution is determined by the 4th Seeley-DeWitt (SDW) coefficient, computed for generic massive fields with spins of 0, 1/2, 1, 3/2, and 2 on Einstein backgrounds by introducing Stueckelberg fields. On the other hand, the non-local contribution is influenced by the number of zero modes on a given external geometry, which we have carefully examined in a couple of examples. Additionally, I will explore how the pure-number log correction to a dual CFT partition function bootstraps the 4th SDW coefficient for the Kaluza-Klein (KK) spectrum on Einstein-Maxwell backgrounds through holography. I will confirm this bootstrap result in KK supergravity examples and also address a regularization issue in the context of holography. Finally, I will present an intriguing constraint to EFTs in AdS4 from the bootstrap results.