Theta Invariants of lens spaces via the BV-BFV formalism

Abstract

The goal of this paper is to investigate the Theta invariant --- an invariant of framed 3-manifolds associated with the lowest order contribution to the Chern-Simons partition function --- in the context of the quantum BV-BFV formalism. Namely, we compute the state on the solid torus to low degree in $\hslash$, and apply the gluing procedure to compute the Theta invariant of lens spaces. We use a distributional propagator which does not extend to a compactified configuration space, so to compute loop diagrams we have to define a regularization of the product of the distributional propagators, which is done in an \emph{ad hoc} fashion. Also, a polarization has to be chosen for the quantization process. Our results agree with results in the literature for one type of polarization, but for another type of polarization there are extra terms.

25 pages, 16 figures, comments are welcome

References in corpus (6)

• Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism
• Perturbative quantum gauge theories on manifolds with boundary
• An introduction to the Batalin-Vilkovisky formalism
• On the Kontsevich-Kuperberg-Thurston construction of a configuration-space invariant for rational homology 3-spheres
• Split Chern-Simons theory in the BV-BFV formalism
• Globalization for Perturbative Quantization of Nonlinear Split AKSZ Sigma Models on Manifolds with Boundary