Perturbative BF theory in axial, Anosov, gauge

TL;DR

This paper establishes a deep connection between the twisted Ruelle zeta function of contact Anosov flows and the partition function of a perturbed BF theory, using an axial gauge fixing related to the Anosov vector field.

Contribution

It introduces a novel perturbative quantization scheme for BF theory with distributional propagators and links it to dynamical zeta functions in contact Anosov systems.

Findings

Ruelle zeta function equals the BF partition function up to a phase

Perturbative scheme for BF theory with distributional kernels developed

Connection between dynamical systems and quantum field theory established

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.