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 $\hslash \in \mathbb{C}$ and up to a phase, to the partition function of an $\hslash$-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, $\hslash$-linear, perturbation, within a perturbative quantisation scheme for $BF$ theory, suitably generalised to work when propagators have distributional kernels.

29 pages + refs

References in corpus (5)

• Perturbative quantum gauge theories on manifolds with boundary
• Fried conjecture in small dimensions
• A cellular topological field theory
• Split Canonical Relations
• Ruelle zeta function from field theory