Perturbative BF Theory in Axial, Anosov Gauge

Abstract

The twisted Ruelle zeta function of a contact, Anosov vector field, is shown to be equal, as a meromorphic function of the complex parameter \(\hbar \in \mathbb {C}\) and up to a phase, to the partition function of an \(\hbar \)-linear quadratic perturbation of BF theory, using an “axial” gauge fixing condition given by the Anosov vector field. Equivalently, it is also obtained as the expectation value of the same quadratic, \(\hbar \)-linear, perturbation, within a perturbative quantisation scheme for BF theory, suitably generalised to work when propagators have distributional kernels.