Weyl n-algebras and the Swiss cheese operad

TL;DR

This paper demonstrates the application of Weyl n-algebras to establish formality theorems for higher Hochschild cohomology, introducing two approaches and proving their equivalence.

Contribution

It introduces a novel family of propagators and shows their equivalence to existing methods in formality proofs for Hochschild cohomology.

Findings

Two equivalent approaches to formality theorems are established.

A new family of propagators is introduced.

The methods advance understanding of higher Hochschild cohomology.

Abstract

We apply Weyl $n$-algebras to prove formality theorems for higher Hochschild cohomology. We present two approaches: via propagators and via the factorization complex. It is shown that the second approach is equivalent to the first one taken with a new family of propagators we introduce.