Remarks on Chern-Simons invariants
Alberto S. Cattaneo, Pavel Mnev
TL;DR
This paper explores finite-dimensional and propagator-specific versions of perturbative Chern-Simons theory, showing how the effective BV action on cohomology leads to invariants through solutions of the quantum master equation.
Contribution
It characterizes the effective BV action in finite-dimensional or specific propagator cases, revealing how it defines invariants via solutions to the quantum master equation.
Findings
Effective BV action is a function on cohomology satisfying the quantum master equation.
Invariants are derived from the effective action modulo canonical transformations.
The structure of the effective action is fully characterized under certain propagator conditions.
Abstract
The perturbative Chern-Simons theory is studied in a finite-dimensional version or assuming that the propagator satisfies certain properties (as is the case, e.g., with the propagator defined by Axelrod and Singer). It turns out that the effective BV action is a function on cohomology (with shifted degrees) that solves the quantum master equation and is defined modulo certain canonical transformations that can be characterized completely. Out of it one obtains invariants.
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