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arXiv · 2307.03830

3d Quantum Gravity Partition Function at 3 Loops: a brute force computation

Mauricio Leston·Andrés Goya·Guillem Pérez-Nadal·Mario Passaglia·Gaston Giribet
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Abstract

The partition function of 3-dimensional quantum gravity has been argued to be 1-loop exact. Here, we verify the vanishing of higher-orders in perturbation theory by explicit computation in the second-order, metric formulation at 3-loops. The number of 1-particle irreducible Feynman diagrams involving both gravitons and ghosts turns out to be 17. Using dimensional regularization, we solve all the diagrams. At 2-loops, we find that all such diagrams vanish separately after regularization. At 3-loops, in contrast, a series of remarkable cancellations between different diagrams takes place, with 9 diagrams beautifully conspiring to yield a vanishing result. Our techniques are suitable to be applied to higher loops as well as to similar computations in higher dimensions.

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Mauricio Leston, Andrés Goya, Guillem Pérez-Nadal, Mario Passaglia, Gaston Giribet. 2023-07-07. 3d Quantum Gravity Partition Function at 3 Loops: a brute force computation. https://doi.org/10.1103/physrevlett.131.181601

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