Singular propagators in deformation quantization and Shoikhet-Tsygan formality

Abstract

This paper adds some details to the seminal approach to logarithmic formality \cite{AWRT} and interpolation formality \cite{WR} by Alekseev, Rossi, Torossian and Willwacher: We prove that the interpolation family of Kontsevich formality maps extends to Shoikhet-Tsygan formality and a complex interpolation parameter. We show some elementary relations satisfied by this polynomials. We also compute some Kontsevich integral weights and reason on the number theoretic meaning of the invariance of Kontsevich's propagator under real translations and scalings in the case of the Merkulov $n$-wheels.