Contents

# Contents

## Idea

The Chern-Simons propagator is the Feynman propagator for Chern-Simons theory regarded as a Euclidean quantum field theory. Since the Feynman propagator only depends on the free field theory-equations of motion (the staring point of perturbative QFT), which here is $d A = 0$, its form is independent of the gauge group and in fact applies also to all higher Chern-Simons theories such as notably the AKSZ sigma-models.

In the perturbative quantization of 3d Chern-Simons theory the CS propagator was first studied in Axelrod-Singer 91.

### As a smooth differential form on compactified configuration spaces

The Chern-Simons propagator was re-formulated as a smooth differential form on compactified configuration space in Axelrod-Singer 93, p. 5-6. In this specific form its mathematical nature was amplified in Bott-Cattaneo 97, remark 3.6 and Cattaneo-Mnev 10, Remark 11. It was suggested that this serves to exhibit its Feynman amplitudes as exhibiting a graph complex-model for the de Rham cohomology of configuration spaces of points in Kontsevich 93, Kontsevich 94, which was proven in Lambrechts-Volic 14. This role of the Chern-Simons propagator is advertized also in Campos-Idrissi-Lambrechts-Willwacher 18, p. 66.

## References

Detailed review is in

• Konstantin Wernli, section 3 of Perturbative Quantization of Split Chern-Simons Theory on Handlebodies and Lens Spaces by the BV-BFV formalism, 2018

Original articles include the following

Last revised on October 1, 2019 at 10:20:44. See the history of this page for a list of all contributions to it.