Appears in collection : 2023 - T2 - WS3 - Dg-manifolds in geometry and physics

I will discuss a field-theoretic interpretation of Ruelle zeta function, which "counts" prime geodesics on hyperbolic manifolds, as the partition function for a topological field theory (BF) with an axial-type gauge fixing condition available on the unit sphere bundle of the hyperbolic manifold. This suggests a rephrasing of a conjecture due to Fried, on the equivalence between Ruelle zeta function and analytic torsion, as gauge fixing independence in the Batalin--Vilkovisky formalism. This is based on joint works with C. Hadfield and S. Kandel, as well as with T. Stucker.