Speaker
Description
We revisit the one-loop logarithmic corrections to the partition function in 11-dimensional supergravity on $AdS_4 \times S^7$, providing a systematic lower-dimensional framework for precision holography. Starting from the 11d partition function, we perform a complete spherical harmonic decomposition of the supergravity field content on the internal manifold $S^7$, thus reducing the 11d logarithmic divergence to the infinite product of 4d quadratic determinants. Reconstructing the 11d divergence from the 4d ones requires careful study of the zeta-function regularization that was not previously done in the literature, including previously unnoticed zero modes. We demonstrate an exact cancellation of all local logarithmic divergences, confirming top-down expectations that odd-dimensional manifolds intrinsically lack local Seeley-DeWitt anomalies. While serving as a proof-of-concept that reproduces known results for the $AdS_4 \times S^7$ background, this methodology offers a tractable, systematic formulation that circumvents the computational bottlenecks of higher-dimensional Seeley-DeWitt expansions. Furthermore, the framework is constructed to be readily generalizable to other compactifications, such as the Type IIA $AdS_4 \times \mathbb{CP}^3$ background.