Gravitational Path Integrals and Finite-N Holography

Coordinators: Alejandra Castro, Chi-Ming Chang, Matthew Heydeman, Luca Iliesiu, Ted Jacobson, and Donald Marolf

Scientific Advisors: Bianca Dittrich, Seok Kim, Sameer Murthy, Joaquin Turiaci

The gravitational path integral (GPI), introduced by Gibbons and Hawking, has long been an enigmatic approach to quantum gravity. In recent years, however, it has become a central tool in the modern study of quantum gravity, providing both conceptual insights and increasingly precise computational control. This program will bring together experts from diverse subfields to explore recent advances in the formulation and application of the GPI, as well as its deep connections to finite-N effects in holography. A primary focus will be on foundational questions surrounding the definition of the GPI, including the role of integration contours, the conformal factor problem, and the interpretation of complex saddles. Participants will also investigate how recent successes—such as the reproduction of Page curves and precision computations of black hole microstates—can be extended and sharpened. Complementing this effort, the program will emphasize new insights from supersymmetric gauge theories in the context of AdS/CFT. Topics such as the Giant Graviton Expansion, supersymmetric indices, and phenomena like fortuity and BPS chaos provide novel probes of quantum black holes at finite N. By fostering interactions between researchers working on effective, UV-agnostic approaches and those developing UV-sensitive techniques, the program aims to bridge key gaps in our understanding. Through focused discussions and a dedicated conference, the program will address fundamental questions about black hole microphysics, quantum chaos, and the nature of spacetime.