Decorated trees for Koszul-Tate resolutions and ghosts

Thomas Strobl

Université Claude Bernard Lyon 1

Thomas Strobl is a Professor of Institut Camille Jordan at Université Claude Bernard Lyon 1. His work as a mathematical physicist is mainly concerned with geometric and algebraic aspects of sigma models and gauge theories. In 1993, during his PhD thesis and together with P. Schaller, he discovered the Poisson Sigma Model; it was used later by M. Kontsevich to obtain his famous quantization formula. In 2015 he and A. Kotov introduced a generalization of Yang-Mills gauge theories to the Lie algebroid setting. In his career, he authored more than 60 scientific articles.

# Time

Tuesday, 16:00-18:00

Dec 3, 2024

# Venue

C654, Shuangqing Complex Building

#Abstract

Koszul-Tate resolutions are the key ingredient in the Batalin-Vilkovisky (BV) and the Batalin-Fradkin-Vilkovisky (BFV) formalisms. Such resolutions have been known explicitly only in a very limited number of cases. And while the Tate algorithm shows existence, it almost always leads to an infinite amount of computations to be performed.

We provide an alternative approach where the generators of the Koszul-Tate resolutions become trees, decorated by the generators of an initially given and much easier to find module resolution. If the module resolution is finite (like for ideals in a polynomial algebra), only a finite number of computations are needed to arrive at our arborescent Koszul-Tate resolutions.

We show how to apply this for BFV or BV in the finite dimensional setting. The former provides an algebraic description of singular coisotropic reduction, which we will make explicitly for the case of rotations acting on the cotangent bundle of R^3.