The Batalin-Vilkovisky construction for finite spectral triples

Roberta Anna Iseppi (Georg-August-U, Göttingen)

Aug 19. 2022, 11:30 — 12:30

After arguing why the Batalin-Vilkovisky (BV) formalism is expected to find a natural description within the framework of noncommutative geometry, we explain how this relation takes form for gauge theories induced by finite spectral triples, that is, by finite dimensional noncommutative manifolds. In particular, we will explain how the two extension procedures appearing in the BV formalism, that is, the initial extension via the introduction of ghost/anti-ghost fields and the further extension with auxiliary fields, can be described in the language of noncommutative geometry, using the notions of BV spectral triple and total spectral triple, respectively.  If time allows, we will prove how also the BV/BRST cohomology complexes find a natural description in this mathematical framework, by relating them to another cohomological theory, naturally appearing in the context of noncommutative geometry.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Higher Structures and Field Theory (Thematic Programme)
Anton Alekseev (U Genève)
Stefan Fredenhagen (U of Vienna)
Nicolai Reshetikhin (UC, Berkeley)
Thomas Strobl (U Lyon)
Chenchang Zhu (U Göttingen)