PIRSA:25120049

Lessons from the Lorentzian Path Integral: Not All Saddles Matter

Kolanowski, M. (2025). Lessons from the Lorentzian Path Integral: Not All Saddles Matter. Perimeter Institute. https://pirsa.org/25120049

Kolanowski, Maciej. Lessons from the Lorentzian Path Integral: Not All Saddles Matter. Perimeter Institute, Dec. 10, 2025, https://pirsa.org/25120049 

          @misc{ pirsa_PIRSA:25120049,
            doi = {10.48660/25120049},
            url = {https://pirsa.org/25120049},
            author = {Kolanowski, Maciej},
            keywords = {Quantum Gravity},
            language = {en},
            title = {Lessons from the Lorentzian Path Integral: Not All Saddles Matter},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {dec},
            note = {PIRSA:25120049 see, \url{https://pirsa.org}}
          }

Maciej Kolanowski University of California, Santa Barbara

Talk numberPIRSA:25120049
DOI10.48660/25120049
Collection
Talk Type Scientific Series
Subject

Abstract

When performing the gravitational path integral, multiple saddles can contribute to a given computation. In black hole thermodynamics, one encounters infinitely many critical points of the action, most of which are complex. Surprisingly, the sum over these saddles diverges in spacetime dimensions greater than three, and the on-shell action is not even bounded from below. Starting from the Lorentzian gravitational path integral, we show that only a finite number of saddles actually contribute. Interestingly, as the temperature decreases, the number of relevant saddles increases, reproducing known results from JT gravity coupled to gauge fields in the extremal limit. We also discuss the implications of this approach for the computation of supersymmetric indices.